Investigating a Quadratic Relationship

Introduction
[size=150][b]We will be looking at how mathematics can model a real life situation. In this activity, we will plot some data on to the coordinate plane and then estimate some of the values that are not in the data set. We will then work to fit an equation to the data and then check our estimates against the equation.[/b][/size]
A diver jumps off a springboard from a height of 3 meters off the water.
The Data
[b][size=150]The table below shows the diver's height in meters as a function of time in 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Elw68HRpaE4VNPaNA3yicC3XL3JVjyITB47xmPv+iLvmhaTVSPNUZ+UVAtVxm99hrVE59beS/11xYZZKJM5OsZeH7mM585rRTlPB6atUvyH9G4hoenKS2e+PTfVreBBgDRdvoMFx+4+NOywntmicygo2eEt8qPv3J6tpd/wuwAfP/3f/+02q5MdSMXnuXNXWPlMTK9OghDU8+O6BvRIL2+oww6/Fa3utV0VATdJjX4PaJRHj0al4SlXVuuMkZ09Hgt7YhX6BSHPiEH3r/v+75v9/SnP33qL738EzaicRS+D16O6omGkZEH/YgP4uMFPWHBxYrZyLTaMf7y65kRnxLeyyNh6mHScRxT8gov0I83nk1o7nWve027VupDbjKmcEvTvC4jzBXZFpyZEUanEWU6MmHGId0RDZSH1Q8X7GEGwGj17Md//McnptjOWmsOWb/kvZbGpJdf2s4zMHKzm91s+sqM8BzapD5r3LU0qn86OpdMo0fnAMYAs8c85jFTHDwRP4pH2Z5Pwox4dGga1NMxgMsuu2wajCkW/LLqSuGg7yTMiA9LwvdBpxVUA++P/diPTXwgL3TiSRn11CY9O+LFWlrlr95oAFS/5mu+ZjqnKl9hS3TIiMYl4aN6yKPHJ2GjckZlJNwEX3/QN3wsY+JvIrMPs6QOvXJOkg/a3uSNQTe+2M2CHfZhWu1lMecbvuEbhkW00s/94R34YO7v/ShGfHwgG/qMceRud7vbhEXwirwkTDiTMj7jgRkgBpi5YRkTbMkYeClXzLHcutbUGnDffmtpTHp0bcBsA2aRh55LqWzA7ByHNmB2ZuDYgNk5mfB00sDMmW83yOufGcjPp+jcm3DxSgs8+fDJx03sD/7gD06udq2NW+dy6z+dNDBzDMfZ9+/4ju/YGzDDg/vf//4bMKsJwlH8+qKy23384x+f9vwNMJju/Ud+5Eem7RlATadaa45C73HjrqUx6ZW/AbMNmEUeeu4GzM7nzmkFZrmqJAN1T8ecX6Ojv8n7pIGZSbUJdVmvEeXiBozgj+1FK738fRAFkLSASMoZlZHwkwBmFhDSzgEiae/QUXNLPogP1OFn6W8lXJ6+OLaDkvrHreVb8ztpYBYarJbta8XsJ37iJ6a8thWzwdmPCEfLTeO0XMvtDmP+5E/+5LQd4wyRczNu77aU6LzEWtOibZ/+a2lMejRtwGwDZpGHnkuRn9YVs8yWzZiX9LNePZeGnSZgpg/78MlAm/o7+5tBN35zd2ldW/Hkd2hgJv/cAqA+Bl2gpKxLi774i0t+feBldSnvATM+ZgNETM7LfMvn5DVyTwKYlXS57BlPUpcefWW9xQfAjImeY8VxP6M873Of+1yNH738y7CTBmbhCbrZkUn8luujRhMAHzxtwOzAwIyyAswwWgcilC4AtGqmUxKmtabV0Pv0X0tj0qNpA2YXLjAzo82sNm16KJfiPm3AzJUVrrsxUDPuSRqBETK/D3OagNkVV1wxfaiSwTXuiB9r+YCXhwZm8/Yy6B4XmAEivkAPf+ICtPJ1yFt5NbuUVycBzEI3Fy/Q7nnOqznNwpPWqpt0+o9xL/7imOgIY211lvyY59l6v5CBGZkOGOPazuRX8sHzUYz4eAxnyMu4u50xu4qDLo4FzHxZRuB8jQiYOaBJkDBtrZk33iHe19KY9Gg7zcDMoVng2SBo9jLfwkD/WqP+VksZbhScznPaD/+7qsEVLfvgw4iP+HKagJkvwr/3e793kt/0sQxSeW+5o7ouCT8twAwQwAe6K4NrXGEG10PxQb76ifL005M4/K8+DmSXdRq1l7jOF0tLRsKfuPh0+9vffjpvXOZbPo/KSPiFAszCDzwB0sILdTY28g+/jsOHCxmYubfSipl6A2b44MaCkg+ej2LEx+MNmFW4RpkCZsCYMwZW0GxjOnOQWUMl2ZG85o03egcMKDVfk3DRMUpzJII6kZVzWoGZgddKJnCGJ0CZGa9VgJI/neotCrpQgZk7+Py9ycUIzHxd7QbxKM/Iw8UIzAyqD3vYw87qrwywXHwxqIQ/c3dRB+lEkt81AczogbIuHRKnIHFdoo0XAEnJozz7CIxMudS6zDvPozISfqEAM/W2Deqy9RLUq28JzNQnPOAuNRcqMDMOG3dM0tX3ggBmCDVbufnNbz5toWSFIYN7r9HKxu09Q6uusGDnf4aMSfydBavl0StfmL9j8vc6GE+hWUGzlOuvZq4pYGa26zJG9XH3j1UJYKRWv/iN6rk0XPtRrIyOqhNqWxcD48ehTeozdymGRzziERNtZVgGXvTFfy2NGVjkE3mWN3//m0hW3OBNebFkHa9Kvq2lYUn61JdLPnxdfNLAzDbhpZdeOl0LYQDDB20VJbakHmvjqL9rKu53v/tN7VHyBS1kpPSrPe+DBgpc36U/8EF/2ccZ1aW0qVf6rNUewMN7ad0vOQcxJT+WltWKJ6/oTbsPVszcc8kI019GpqRnyTNwNQebS8pIupI/5XNvAEbXUuPKFDzRJ574xCdO92a6THQfpqQ3z9GJ3kd0Ck+6liuOcQi/7n3ve1+tLy2tBx7oj/LDC3yxjXyTm9xkaRbdePKt2bRzN3HxjyXzPPRp12bFvycXozLKcPnhOV7gjfFD3/zZn/3Z6T3jC/+MLdIwzesyBGZQ8n+KX//1Xz+t8ARNc0cmFY2rwlaqgKP4cX0lY8B5wAMecJ6/MEJ497vf/ey5mjKd55ExoLlbxuwIc+yl+xDge77ne6ayMO0kTOh2EBVYzDsXTfe9732bM7cl9VxSB/loN8LCZFC55JJLps+nT+JOprLe5bOvpAy+NeWRjmdg3Bcvwi/5KZOsp4O4SkV74Ec6lTiZHCTtGres+5Jn4F3bnSQwQ5dVulve8pZT/0vfV+/I0BoeLE2bszHapSYfS/i3tKxWPOCc/qA3XDKbMsnHSekQtKXcrAYBAi7Njr+rD+iTvM/dVv2W+stPfbn02Nd+7ddOF4+X/kvz6sUr6U7/L/2WPI/S9QZg+S814pIPOsRuzBOe8ITpf1WPkkerrFo9A8xqYcf1y8Qn51fLfFq0zf3VPzqT690/61znOtdpymPKmedVe0/cuTtq58Sv6Q4riK973evO0yv0jDxhhzKNfNaau9zlLtMF1eQlOsW447k0JwbMFE5pcMOouICfAQdAi1/pWsGoCYw4I3OagJktOQ1e1i3PeEPJ5n3ujuq5JFyepxWYRUkCaGVn8OyfG/AtKyNL6ro0Dp4o4zQDM9vvWWG9GIFZDmoHmOEFOckW1byv1N6XykMrXpToaQFm9CiAmEHJyqZJX+1MZsmPVv2W+svrQgNmmdCVfPAcnVM7SyR8qRGXfFyowMxxGiuw82MC4ddSPlxTwCzjQ+htufNxJWOL+GXYRQXMnPXyv1k1plEwBhwCUgu3FfmZAMwo0Rb4ipJoKZGlnaMXD29PKzCz5I0/tS+oMkO8GIGZmafVkQyGFyMwA8LIBj3hOdsO+gp/23c1vVH69frFkrDTBszULfXHg9gRL5bUtRdHuZHFC2XFLHqjlAfP0bkXMzBz7tr2mv+knvMn7z15KMOuKWCW8SH0ttwSfHm2Uibt3D8THl+Al2HyXWtO3YqZVa/WIUuDDVtjqIEJo6IM5nFGjDotK2ZRoiMl0Qof1XNJON6dVmCWdi07Qp6tBBh4wpsldV0aR7nKOa0rZm94wxvO6zf6CT90H9oo4zRsZWYGawApvybTbgFtkZ+Wu5ZXpxGYqTtQYZUsfUQ/6a2areUD/kYXb8DsDDfx5EJcMXMeTJ+af1w170NLZeZCA2b6ij5kXIn1jwiZ5FhEsRJt7KZr8GWtOVXAzLL729/+9irwUtkeMBOeG5vnArOEUacFmGn4ElzM65LZG0GZhy2p5xKBkc+FCMzwzcCzr85R8gpPTisws4XpYHUpD2VfKetxiGflniZglq1M7VXaKNiST/Pntfw5bcDMYDrXFQBZBpV5/fO+lg/y2YDZ+VzEkwsNmLVA2ZVXXjkBkcgLd6m50ICZupV6xHPOszpaNA87Ci9aPDtVwKxs5PmzrzANNr68nIcteW8xIP4XGjCjWGv1Tn3WuPK90ICZwQdP9jlrKXmIJzrgaVsxM5kxY0NXKQ8bMDsflGm7ERjBv7XmNAEzfcHAUcpFngPO5qAt4Wv5IJ8LBZhFd2SlPTyIm8nwxbiVSX5qK2WvetWrzu5MhE9LZeY0AzOA0+rXHGzN3zdgdtWn1T5VNdjkbqYIw1J3JDQbMDvHITy9kIBZLkR0biYdSB32aeQn79MGzHwQU/sY5mIEZhlgeytmrQlN9MhamTlNwAygYFO3ufv6179+Aqtzf+9rjTwuFGA22qUATvwtU41PR+GVuKdtxcwRIH/ZBcTP6/e85z1vugJnfrTI2PCQhzzkammWysw1BcyiH+a3PaTevqZWLzqCTGQsqbl2KTLRg0nKOEeRiRbPLogVMwf6M9AAUGHkUdwWA+K/AbNw4syn9hcKMKM0vvVbv3UHoOy7c5zjyBmeyP80ATMDnzOZPpiZ94X0l30oiZIPtWdlnIatzPlXmaU8eI4infOqfK/V7yh+FxIwM/jU7qPah8zI4zQCMwe1AdKyzT3jg6/25v6Ai8tla6tGibtUPsQ/SWCWrxBbK4Ho8V+g+oUzZKkP16oRf3V3PKS0/oZIWBnf81JzksDMVmz+T1Ud0a0u8UNLWQ87c3YgfGA41x/etR/e+BNz8VgA9lSeMdMBbakQgHvc4x7TRbOW+lRYZUamZEzt2Wfv5UBTi7O2DEDExZxPetKTpi870e9OKJdmOrumAU/C4CHhaXWmLKvXOga+rDXy0JbaNBeF5kvXe97znpNA+trt0EZ76ATowXttwKIt7W+GA5i84x3vuFon2gcvanVM2VwXiJJ3dLLoI+9o5O5DZpQjr5pVpi+YrZiV1t+Kpb/Ev6R7/lyr51H85Oceohvd6EbTxZFoDd3cfRl5kb3IhXe8Dt/JjM/5eytm8wFIHqVdS6u8AMTLLrts+pNjeoTRn/YhD/Iq6c0z4JCb2uNn0HUvY97nrsFl7dUHLX4pS33V278xfNd3fdfO34QxGRtaaeM/p3f0Tie29KK0AVnizD98wAf+2q4sx9jj3xPUpfQvn0NvywUO0vZooLfwwkqcfzHRX9aa0KNvWP1y2XvAlHKyelr2HWle+9rXTvHmwDNpe27KjLukDuLqs5GByAj+X+ta15rGHOEx4qfveF5iQg+XTtDWLSvvMv6+npfQ2Yvz4Ac/eBrbLBhF96MNvaFZ+u49ZhISNszVAQ0GUUi9whM2YgaAlIGmFTd5tdxWuvi7FNSlthCwjsT6pwG3iAMo6Vit/PflvxSYtQaYtXTgh47BjZIi3N61rUEPPw5tyJRyoxC1T975oREoi2KL8IpjaxO9hzZzYAY0oANt6RNraVCP1K3lilPal7/85VN/eeMb33iefxmnfN4HjbaRb3jDG079Rn7yjwLxvA8Tnn70ox+dQAgg4kyIwSa80WczkMaPSy4MvC0gEn7sg07/CmFAe9zjHne2r+DFvnRIaC1ddWN9LRZ/5aWPxC+ugXg+GCeMu9bIQ/ms9rJFhBYm15iMyijpqT1r9wAObkBE/N70pjdNcpG02sDFruKRh/jHxQ+y8573vGcayLneAcvEqbmjehgL0/bKNVbSo/5VxqW/6FpranSdtN+oDqGHfgwwwwv9Uz++9rWvPY052jVGmsiR5yUm5VyT7hI6e3Ee/vCHT+fp/TME/qTu0SN5XwzMAJl3vvOdZxV0r/CEjRioQwNmvYEmebXcURmEwdJvVsysEr3oRS+a/mWAItlH52nRVvpnADGbrdFM6VDA8z/rTdwyr+M8ywcvuAFmucneEra7svDjJIzOyuIJ4dSJtYNZp5WAOSgTB7DNauOhaaRcbYHgD55RNmjwzI0yXkOHdpCXiYLrYAAL76VN28fNhzImSPHruWvok1beBq+smMVPewlDK3eNkR4/5fWBD3xgd6tb3Wqy7373uycgnDCrZ1bN5ncLkTX7+IAAACAASURBVNseEJH/WhpTv09/+tO7xzzmMdO5JJMY+UahJs4aN7SWrroBHOpf+uOLutMb/k7HygHdMeLFGvqkRUP6qzKtIJrIMKFxVEZZj5N61nfL1ZXIcK/8UT3or4wfAWbaxA4NHZawUT698B59JxXWo09Y6MBT46u+nEksPnzJl3zJBsyuYqK+DPfMP2aLHsFLZhEwcwjO3yVRlhi/1KTBaq5B2HYRYEax1OKEyF55rXTxJyC++DSL0XnQ77+qbGUaFPfReXr0JQw92QsPbaUbYEZ5lP55Tj7HdeUTIAaYMZQV88AHPnD3whe+8ESAmb+LsXdPmVuN0Zmj6D/4wQ9Oq3dAitWx0lJ4JwXM/GUX+cAv8hNlE2BG8aw12kM+ZD+rxt5Lm7aP+9KXvnSKW/vrssQp3X3QqA1ufOMbn52QoQ9PlKPvcNcY+WWC9KlPfWpnksA6CwJ8CCMf4gknB86RUGwuI/aXKmWdW89raExawMPfu5nkAWnhwT74oIwW7SN/eqylN+ZpU5fjuvJLf9VG/gmB7mJOMzCb82HJ+4hH0QfiBZhZ7TXeXGzATP/UX43rnulOLv1x/etffwNmVwnTIx/5yGl1ly6jN6I7uPhHLplFwMyyrMHbjIwARqivKqvpJF7NNdhlQKqFx6+Z+VUBiddyKREI9alPfeokNOh/yUtesnvQgx50dsAdlbGPcPThn1Uxg01Jr0bxB97CSv/yeS0N8tJpuAFmBIF56EMfOq0iUqyHNh//+Md3hNNWgj8mD/jRgR1IxYOWzTL5oWm0omrJGW3kh8xQMhRx2mQtDfKRJ2vFzKWxeY+bsoAQ2/625MU1IDqjMPpgZh80aq+b3vSm5wGzDEgBTGvKUVdbhFzy6GMPNmUA8pl9hy9zN3zquWtolFbedJbVELoEXaGZK3yt6dG/r7B90Jj2MKmwgmhSx1xswCyDqrYJMLPl/qxnPWsCZtGva3i+r3Zfk8+I/vRH/NBvudGZdBX9YcwRFoMe/GE9LzFr6rCvtEvo7MVxC4UdGbpb3aND8azkxRCY6YSAmUNrLrsMIpbRyPSY4YuzkwBmKnv55ZdPCtVAi/6Xvexl09kI70uFYlTXUXh4YSnTDDPvXAOv1bRD//nwHJhlQEETsAr4HNqoqwOyWTEjX+z73ve+6QsYX8G0bOg9NI3kw5/64hfaIvMUy77kRT5RaOVz/FJXYce1a/mkXIr1K7/yK88DZuEH3qBzjVEGvsqLkvLMeubnma4p+TJ/XsKfNTRKiwb1Nug+4xnPmAYadNAvoWdtGUvqsTbOPmjULvjh5v/HPvaxU3+V79KJ09o6nFT6Ea/QwXADzOzG+EjHihkZXmtOqq69ckZ1IP/po+qsT1jFlacrLG55y1tuwOwqJppYO87k7rzoO7xjFwMzESlGQmaFw0yWckomowbrNbb/vzwJYIZWytQ5M3VBv6+arBJRMCdlSl74EAE9Vs7e9a53TbyNIJfxyue1dOo8lIc8s2ImT++PetSjdg6WnwQww3NblrajlOc9MhUBzUBXc9F7aOOSxSc84QnTCgnwjm9oIz9pk7U0yKdWv9IvZR3X3QeN7vW5+c1vflY20GflKPzgrjXqFxlIXeXLz3vJk9pz0vTctTRSomTBpMoKvD6ERv5cunKt6dG/r7C1NOJ/wLLtGFu7JnXMxQbMwsv0CbrMcQMyYszcx/iyr3Zfk0/q2XLVP6AifSGrpw653/rWt96A2VXMM65cccUVEz8y9uFd+BYeN1fMNGQQnbNADnm+//3vn5RTFFIyabmlMGg8X/E4r9azZRrPIzOPP39Hqy92ACGMoFyBEEBT/U7KzOk66vtaOvG/Bsz424545StfeXZVZG1ZvfTq7XwOWpStA+fr2Ago/5aV/tDGVRUmDsAyOgERtJEddO2DBnm06hh/cdbYtXxSthnvLW5xiyowww/9a41RBt6yjPySZ/zDj5a7hEdraJSW7gBInD800bP9ij7+6N2HLllSj7Vx1vJBG+AD16zfJNMKM3MxAjPtof3pCLJg0u8c5MUKzMiFvpDjOnZILrnkkg2YXdXxnE+13Z2tXeMLfkXXpX92gRmB0wl9QffoRz96+m82mWR2m0xOs6vj2Hpw+B/t6gOY+epORxJ+MRj1jABoP5bBA8Ji3zsHmsWt2RGfpCEzGUC9zw0/dCQstEjDb4lN/odyyYdzcLZqgA80kht0L6VzXu/5u3zSGWsuPh7a4LVyetb2uq3MnD+UJgNz5KmXXj1Hpqxr2jRpenknDP/Q0rLCR3KV8lqusvQV/cTRCH0FH4B3/kvKGNEg/NAGf8O347jqmb6AB87cAavyyiBz6DosyR8vI0s1d59tgSdkQP19FWshwNEMfLqmjbqjrWdHcjfilX6nruE5WfDOBVC/8Ru/cfpwBw3iCKNTvUsb/x6vknetLfkJX2vQ29Ih/LVzq/z4j2iAQ5zJtNqMD+GTvNmYJjATQWUxzSWT9kZf8YpXTIRBwxeSwQxL7ulAZjXf/u3fPtUNQy8Wk/ZUX0qV0UEAV+Cs9Z9x0i2xeInHBNyzNHMjbGQj5Id0ezS8+MUvnr4MtMKr45gNZ9tVf+ilTVit7iUv1C1xa2741+P7iD/aoqdoomzEa1mHVK973evubEnghfqTmcSv0V76iRcFdFxXfr26Cu/VEw0lTbXnJfxWb7rEKpEZrzIDRrRTj8YlYfLr8Ug9Ribt0nJ7fBK2hFfJGyi1eui8KJ7GfyT7kSH8PK5dws9eHPSio2dHvErfFE9ZZMF9c4C7L4a99+qXFfgencJSznFc9RzVY9Tmo3LxMP2ATIQf8rU75h9cjC3e5UXG1V08ftKrZ89IN+JTry2XhGkrur5ljQHGzZ61Qtiz7kC0omrSjyb1Z7j4EbMBs4FAhFGfCS7hJgzMcYCZjlEb1OZ+USY1ns3jHvWdAPcGryVhlELPOjPjDKIrCHQWcSkevJP/EppHyqzGm9JP+lE5I0UVpddTSiN+UTKAWVYPxY8Slj86e0YderxeEjYqQ/iIF2vDlWHQ8VGIM5n4Ik/14zLirLHaqccPvO+15ZKw0NviB3nvyYQy5CGO7VxfqFo1IxP8whNxWjb9SZrjWrLXs+jotQXalvCrFyf1U2/P6vXWt751+rjJitmonsKTR8tttdNSfzwa8Zhc9yxQ1QMbjjuwzqM6O+yDIR/3kQ/AzCKIS31NdIVxHY/yxTfrPXdbtlznkt1q0LPOa6+xrgMDqFtW2T6A7Fn17Fkf2m3A7KoRY1sxO8MIioqiYQ4BzCgB+VPubE1xomGNocB6s9B9hDnA67qMT3ziExOpGWy46rWkDuis1T9+8uoNHCmzpbD5U+w9qy1SXs0V3ksvzMrQl3/5l5+d8Yb/8kOjQanHc2X06rAkbMTvJbyq1b/0U4+e1e52Cnzu7mobA5H0/NVxHxYv1KVlldejUVhZp9ozOnt5aPNeewqXrzhWUwPMDOz8hI3adNSeS/RDa1Uj/j2gIcwWvVXgljURAS561sTNBcxABl1h2862rmMQtjTdZuBC5JYFNnqDvDBXCq2xwIS/tuvZHpAQBuz4Q/SWBWgAUWX5KygXYAM3QJpL6V1/5MC7f2yQlz8d9x+8+Vs5/i6Z71n/gyrvlhX+lre8ZZV9+9vffpam0Fa66j/iVaut4+/evw2YXdXDN2B2hhEUIsXMHAeY9YCEMANKOUAZtFjKOs95rw0aiVfmMX8W59DGYWaXnJrtKd9gFPopfgNb3ntuq478R4MwXo74jZbeAITuOf/K9x7tCXMWwl8ylUvvypSPepiN92gQXpZ5nOcRL/Cyx2tho3JHqwpAh3q6S86XVQbsAJwRmOkBnaOE2UoBlFvWCoVVi551X6AViuNaIES/sLLhiIvVQ+eP5ctPWP6lo+UapICSnvUvED3bWtWIvwHVQNuygArQ0LLlgNx6DhCwSgZwcB35uetd7zpdmfG2t71t5986WhaY8KHRIS0g0yo//oBSzwIjPvxrWe0MoGp/YBIg8wyser/NbW4zAR6y8clPfnLyt1Jm9UwcssP13rL0UE/P0IXRWWvcnh6hQ3o0CPMhW886UrUBs6tG8A2YnWHEWmC2BBApozRzcJHBrOUaqHqDpHStFYV9+Tv87wJi/0CAFgOicnV470sGYrT0zJwv83fpe0pC2JzX8/JGgEV9Wu3AXz2tKFgxs0Kk7vyBekpo1Fbii+fDgTXWVorVmZaltHsWqBwBEYCjZw00Bh9/HA2MAACAg8FKmNUSKyRrrPxywW7NNUBanWhZ4KAFNOIPkLTACn/gwmpGy1rV8AX36173umnAv9Od7rS7853vvANCgABhzvD2rP7lvHLPitOzyu9ZK1b+FaJl1ROw7Fnt2rNWzAAKIEP/ADqstjuDiH8G6B7w1pcObeiI0QrmCMiM+rnw6Cp9HoDxrlygi4zoH/Qok7ie0UfPJP6I1la49D1eLwlDR08fChtN8OZ6fP4Oi2zA7Cqp34DZGUYQEoLFHGfFbAR8yk6jo+jwEeQIfBmn9pxO23NHdKwNN5OkXCla9FOwOq36cPlxexYgoYhaFlCxNday2qcFROLf2oaJv9knxdiy2YZpARLK1Iz3C77gCyYgYpASFxgxKzYDtvrRW9kQ1lsZWRIGiLS2UfgL7509AUpGqxKtATz+QARQ4j+DHWZ2V5VtK1s07r2Tfw9I7CNM+b16aqsRMNTmLXngbyWwtSLHH0i2IhcZc62MM2b6CACsz5Dpltzz13/mA9b8fdSHo1daLv1R0y/xi37qgZLEbbnRA5mkWLUB+FygrS3ovF495Nui/yT9e3pMGDpH9Qi/8VNc79LSE77K/PCHPzzJiLEnY0HaHN/UV5o1NvmtcXv1RJu27tleemEmdhswO4NHpi+ptq8yz31le1xgpvPoRC1L6Tq7EQVuFcOhUQrbjJLtbbMIMwvtrW4YPMxSD2n9/ZFVEaADPVYvLNcDKhTMEutcSO88gjx7gAb4cW6jZ22ltFY2+BvIs11Rc60qtP5lIf7y+ZzP+ZydbZeAIHn5+sz2h7+SquUdP+dHeis0S8LwoAfgtFOvTbRbS2bjb6bfs5Qx+XcH0TOf+cxJLoBn6fkvmZGP4hgAR4PKSPGPBjb594yBtceH1EEc/fvxj3/89MV7wEkG8haYif+oHonXcnvATxg6AwBqLjp79RQmTs8CoHSdiRK9R89ZKcQT/QJY7bUHuVmzkrwkrXqMzKgt1KEHYNUDj/EcTeJ7JhP0pq1MfRSoV5Y25TKexZWmR4cyeu0lj176JWG9tkrYKJ8en4S5/WAVMNOBESEzM2XnKizTeif4+zDKaHW8+O9DUUGpvqbSUQiOr+58KUKx9hp7aViUe8tVpo7bs72vXgJuegdRgR7/XdezgI9VFPmYWXMBHPzxtYhO1EsPpJSrKwFQZuGsATCAAvAATswcAZTM9G13AAQ9m1WKmkvxAU5rLNDhr1Na1t+P+d9O4RSs/850hYZVE37ee1s1woCiHmiy9ZPtpZoLBIVnLVdbpA1qrrbutSdFGYXTcsW5yU1ucvZMlXgGJLJu0KIjemZJH09fb7kjHSC8Z4RT7D2r7J7SVW9x/Em1y6qtDKk/I53wtQadPRqEtXgU+vdBwxJ+K8+ZNiDVBxF4y28pr9fSeRrSp63CL+DAipk/MbfVjR+nwYS+ltvrF8JGYIPs40WwgXIiq8acu93tbtOkji7BE3wC5MSTPzzBlU/Lyq9n5CXvQ1q0jXjVo1GYFWYrqvRy6hzeyT+meV1GGKvCMqGM/AeY2QGAAw2PZi3CxWtZwKh3NkRYlsxbLgXZWz0BWKyW3fe+9522PGy/uCTyDne4w7QSAnT2ZuNLwszoa2dC4merpXe40gA+GugDCICCmrWlYmulZf0/V7ZegBoDjHxcdge0ftM3fdN0/04P8KDBwXi02ppxngR4so0DcAExzrA4LAtYUE5AGT4AbFaInMfotZc2JxdrLPnsWR2CfLes9jDrtQwfJSONZ9bzaTChZ407qgc+Xu9615t0QAYa5TFxR3mM6FubfpT/kvClNOhHlKtJigGmzHtpHmWa8nmUXngZ/xDPS2gQR98xYbQy6n9+maX94hB0HyLPES/wABjhGlQ903U5YzZKL3wt3SdRxojGABb6odST3gGze93rXtMZxMiHBQ88Y/Qh8UZl7CNcmT27jzJG7QFH2fo3kVZvFg9M8lK+PIbATCTAjLD54iQgxEDb+lol/gbnnrVS0PuM11YNMNCzlgWd92hZB2L90S7lARwBWv7rzr638tXH6sYaK18zpZa14mE1qWWtfJh99uzo3EZWL1qCp/MYZLP8ndU7bQuIWBEFiiIcNZcAyQMt8gG4dbIIFhrKdx1Ruel46Yjit6w8alsP+/RDT4tP/Ddgdk69aO/rX//6GzC7CpRvwOyMbOgnGzDbgJlxYgNm5+4vPKc5609WmF3oDpjhm36UMS9jrpRNYCaSRAzUa9UJMAPIWACnd65jSZgVCV++tSwgAwT0bCqH1po1i7F0aAXELBf4scpz6aWXTtsRVvWCXI/r1sot/dDQ2ubkD8ykUY7roh0Q6lm8mudv4AUs/V+mMxI9HpR1aj3P05fxlH0aDDpKuubPGzA710oA+A1ucIPpfKC2jfyIgW9L2jRpWu650upPrXT79K+XfM43ZW3A7AxPtP0GzDZgpl9swGw5MPN3Xf4towRmxmwYoTRNYKbjRRFbVbFv/rznPW/aYgKUrJZokJ6N4o5Sq7klMbVnefSsCvXAiDrYssMQIMS7A8dW0Qw6NZqO6tejLzyo1a30U4+eHa0YaYeeQYd2s1KVVS2gEBhz5s45AO3cqzsasn2dlbfSFVZbCVNebPjRK6dXj32EjdprA2bnuKyfu8fMecS03dw9F7v+1GtrYSMzSr+P8KU0bMDsDKfIwAbMNmCm7500MCN3x+nz0fvOGNstc92Kc7jxr+XpqJR4dv643mvx4jfSI9nhcybbeK9s/INLStMEZiIaiCV0vstWofNFCFhqQmzP7eWFBmCqZ1UqjK25ygYo/UeVL/ps4TkT9cAHPnBaCRydg2udjyv9nYfqbUMuAYA9PiwJU89a/Uu/gDd+MYTDitlDHvKQCaT12iplJE7yiMtfm6XMWjzhPZu0a9yU23JHeW/ALC26mwD1jW50o/NkQ/ulrbkj02qH+K9Nn3zWuEtp2IDZGU7pQxswOyww8+GUD464Ldkeya3wMq0z4na+Sr882+WqjVVokC7x5u5JATOT/oc97GHTR2pzGpa8+4LWvxAY78gvfOOIkzwt7pR5GBf5CxdPWOL7WK6MWz6P2sNX3c6DA2YpM+NRmbYLzBDHWFWx4uSgOEBiT7Q3uCZMgSXR82fxlNGyARIlwfNnQMvXHi1rpQYjHLpzhgrtGsZt1dIuKWNe5lHf1Vs5PXvUPOfxNXJWs2qudhNHm+AJN8YhfR8AAK49EEwwa6Zs11p4/Mp4rWc8aslD/Ht8FBb5a7npCC13A2ZpsTN3Dt34xjeeJmfaDM/CY+1RytG5VOc/tdo6/ufHvvpb4h3SvXqp5/uk7A2YneGLdt8nMDP4OzjvA6IaOAj/Wy7dJo9aWqsiLWAB9NhRkdYuCjdlnC8BV3/Dg/SB6K19HP4HnMq6OP/8gAc8oArQrk7V1X1SH66873jHO56tYxnmwy9hc9sCckmr7vhP33Lj733t4X/8NV4DQ+4QBKzcHpAyjuLKw4dr2i3WmCZPZ93LvJwL5x9QlrDEJ1PxK92rc/98H4tbvvAHzOZ5Jx8pmsBMJIxlbGNkK9N2mIEdw0YmlW+5yjgJgxGWECFuZVqW1EhAGtqyzXZcFy9aIGCJP8HuASJhgFWPvrJDpIHnrnLUl/JSd2n4EXx/2g2Az9PU3uUhnXoTLnlli9Rz3m2Volt55EY95Ncz+CXvnl3C016cljzGfwNm51pIG7suI9sHaXv8JT/eR6YmQ6Xf2vRlXsd9XkrDoYCZAUO/GZmyfuLru666Yek072Wc8tlZXqsAXO2ZD6LKOKPyE67d9wHMDHAlGEJLgAj9UdLWexZ3DijyXgMWZHd+nEUe+CMdukYGD/SP9AnPa4EZWmuDvg/W0GUcLvkwolF44ss3PIlf6ZbADBDULnaCyji1Z7oaP6MTEsf7WmAWOeMaS44LzFwCHaAlr9Le+973nsLkj3bt6BYH8VOX0uVPTsQr/T2PTP4ZAzDTf5NeutDkuQnMRIrQGbBdMeEeM/6MDGXcsxqrZ+XfG0CF9QZoYalYy0WvrUwCjxlW1tyh5S93CCrAcDEY/Am/ADy8jXGnFmDmjFmP32n7pItb8j5+LZe81M6hxa+kq5XHWn/16NkNmJ3jMHm46U1vevaLXXyLjADlLZk4l8O5gSFyYvWCYos8lnFrz0lXc30B7gqcWhhZswLjqAFjZdi1LrXVk1q5pV/yPwQwy+ycbhqZ0KFuwFwAM3+gzKABoCVeXGXc/va3P+8cqfYDzsr4o/ITrt3XAjO6F1AIjXEDskoZSVjLTZoADy5gYReglgaAAkTmYQ5lJ4/UteXiQcZIsux5DTALP2ry6ThR6CppbtFW+otvDDcG1vJIfvgRQBq/Ja66HwqYleUHmJHl0n/0rF3Ikr6hzeYWv4UlXztp3tla3vqMMPHm4SXfa8+wB3AGi2ShKHkY+9DGNIFZMhVZozog7p/RvevQTDK8Jt3Q2XIJjes2XPfhWgrMcPeOS0R9WYr2kZk35Px9H/Wf53mc9yV0RBjkT5nhj7vG7n73u09Ku8eLJfkfh+59pxnR2aujMCuqvuK1vI22gEmyn1nVqIx5nYADt+XHX/qRERdYdhlwrqBBk7ySz9ylwHV6+dvSBrpbwGUJDers8L8vmuWX8qTNoOT5KNbhWwME+VtCQytvs3kz+1r9TD5MyAx20pd0S6Md48ddYuTjADDZAPKk03/YJaZWD/zNoAGY1eLU/Jz5rcliBpRyuydlSDPPSzxplraFvMRl6BL8uOSSS87yYikf8E67kQOAoWwL9QqACF1zuufv4klDThnhZZ7ls/HrEY94xGS1XRnmOWXXVq7m5Xpn5CkvdzUaJ63QLDFlfuEH+Yx/aCt54h7I+Cdez0UbHouTuiV96QJm834hvJe3MDKRflCOL9KSaee58UM88cXxzCgPqOPfM8LFjXx7X2pH6dAo3/QPbq+c9JnEL+no1UEYPpgIAfB4hhfGl/BQXsxiYGa17LLLLpsyCDAbEVESfKjnEQ0qbCsTMHP9BtrNoh1214mWmFJ4a8/7qFst356fAYct4yyhgyAw0lFmhAMwu+td77oKmOGzGXRp5/Qpc0SjfGw7+3JWB7AqYCVAu5V1zbMyyvg6S+K3yhq1ubvvDL5AjXJKYAacMK284x/64uo/LmjOu3gj4w+W73GPe0zbCUlnBYDidsFv/OKK70LlvIcWPJlvFyVsRIP2CDCzJZ28pTsOMNMH1ckAkUF3RENoLV1lZwWgBsyAHdsoSRO6ufq/NKXfiAbh8vLXVGTDpdHeMyAtTR964pLvDAJLgZk+7J8p6C/tk7y4WX2Tb/yBFWXUZvjiCEv8UT2UZ6Bj9EnA7La3ve3ES7xYYpSJ91xbcybIZVvIn3y4mFTfSz16boBZZKrMb/5MjuWtDGXNwwNeanI1pyH1Raf6axOgz6rIEjPPj9yy8Q9t4QnaStlNvJ5L9zjYL6/ULfmW7r6AmXonX5MnwIz+wR90HgeYyRMP0ld69Z2HjdKdJDAjF7CIf8XBD7wIP8IfdT01wMzsBIFpOO8168uKkvEj4ScgVvtcoGrlgTKxckH4KYQlJkJWugEgQIHzHc5t6PAlbUue5Wl7ZA5EyrLKZ4ON8wZZQfHsklz1WlIeHsdEIACzO9/5ztNAlrCa28ofELrPfe4z0RRa0WfrBL3x47by4C/cAGG1o0yD1/k6pvSXt3acxzcjSfxaebW6lX77BmYGRmCEDa3o6hmKPgBmPnhEuSYvPHF+T7117vAodQdepcl76fZoELZPYIY2INHqLHoyiI5oKOnNsy+rrVrJpzaA8gcCEz884YpfDm78lhh57ROYkV/8cOmkAWcpMCsHmnmazObll7orw7t08SvdcrAb8WGfwKxsk/LZirD2C1gsaW09HwWYKQug9E8oZX8JDcpuydW8/PBrX8BMPdIvlBWatF3oorfjP6dn/m4iaeU4k6jkkfSlC5i5DsI46dnxJROQkp55/t7JBD6yGV+Sb4CZtszKGL0lDSPv+IeXLbeU+xodLb9Rug2YXbW9Yk9Xw5vxsoBFDZg56xNBMliKM5/1tRox/hrLjMEslzImBPI1qzkuMMtZDltGBFAZlKtZLGXbEpC5v7SXX375eYCGnwFWGRHuuPIGdoDT+OkIwAkgMs+/9p6Ogz9ZhQLM/Heo/Humlh+/KHYdIHThswOU6C233lp58Nd5s0WUfOLiiUEn71yKo+RFwuSV+LXyenUUtk9gRiGWYCQ8QlfPUPQBMEmT+qVPlOCCAnSYuRxoyrpLU77nuUeDsH0CM2DK5AU/0BOFP6IhtMb1t17y8i4ffEhYXP74gf/8wjuur/BK3vFbYuSzL2CmTHzQzgFOc5CVusxdddK3WOnL8M8EYEYPkH2goqxb75ksaXN910TOarcxxurovP+UslB7lg9LV/bKFBazL2A2Ly/0AUtoouvjx53HL9/1XaCsPIKQupV55Bm/XOcQEMe1bWqFPn21zD/PS4CZMRiPGHkFmOExnSWvkdGOGWtS9hJ3lG4DZsW+MCGIkLSYa7ARRydtdZJRYwonFJS0fxoAGPx10qMe9ajpH++XpI/gcoGZCEf80Z8Dg/7Ql3+rTqU/BUS5piMkP64ybFvFj/DKGwCMX1yAVXwrM2X+82edQaeIUa44tj/w2WypZ+b55T38mCtAwEkYIB5ak6bmGqDKOicN14BTAjOzLqCv0UusZAAAIABJREFUFl/eiV8rp1dHYfsEZg57WrEKGAmP0DUyFAbFWIItvEi/0SfCo/QV25nxS90B4/LcSvyX0EBm9rGVaeYdMJW+H2U/4kNJL15IH2WOFzVglkmdCVgmUPiin+JFyTv+Sww69gXM9P0cNj4qMCv5MX8OMDMxSVjyJ3vxK93035zP6vGCPMiHoQvXbGVGTrn5/1yTdFf3uAmgpHH0TJbIglvVS30KmGnv9LuyzNqzM5zykW5UpvCYQwIz9TF+qVsm06G9R6NdHHKWuNzojtIvzya5Je/ij38t/aF8MqE/svoVk7RZMXPOm85mAhQ9q4/0S4w2jKz26j0PG6XbgFkFmFGgc0bm3cFngkSxxG/uLmlQwMxfDn3oQx+agJltw7zLb2QiZNwoPgIS/9CULQmCEL+WS4CtsKVuySuu/K2C5d3fYPEDduJXuonfKo+/joO2GO+MVapv+ZZvOTYwe+QjHzndMVMqDZ3N33ih6yjADNjysUlZN88GgBKYKctWXy2+uuKd+DV+pP4td1/ADBgBzNAfMIL/3tE1MnMeeKfcMnCU4VHeeGJrPNsDQInPwcttvZInIxq041pgRtaf/vSnnwVT4cVxgJmBpqwLXtSAGdk2kAnHk6zOG+DSBiX/RnwQjm/7AGb4YaAjw/IMcFq6Yla23/yZ3OtzVo0Slvxbekl8Vn8ZGfIQHYL+fQMzAM0qD32nDVOHkYsuE9SkKduWDOB36Vd7BhicPQPKhI/KFB5zSGBG5ueAM/S3aFQX4Bw/EpeLF2zpN3oGlqXB31p5eK8ctgXMrMRlUSBHfvAueip87LnkLrJao6PlN0q3AbMCmD3lKU+ZGhuibjHUChGByEy7Fq/XkAkDzKyQOZhJEMyKKGhATZ4jUwquAdBycrmkLA9xnvSkJ02C01KAJf0RlhYwkz8hzAwmApm/xilp8pzwsozyWRx1LzuFDsUAEADOcVfMdMh0sNBFMaAJT5QT/5Km+bOzf9L4EEE9ky5gOLxIXr34+IeueRneR2ZfwIySx2/0Boxod+9L6Eg9S9eg4SBt6Zdn2x3OO+ozgIit+mzh1/iwhAZtsBaYobns5+HFUYGZ1S4fUKAp9VHXGjATDsQakMWJdV1G+FW6I5kQLs+1wEyZLpksV4QCnNYCs/ST+YQk+bf0UnTHNQnMyrbQZ+yS+Ho37XxUt8yPzGh/RzVK//kzAGShIP5LyozcHAqYkQn006+hq3RbNJoQOvAvvIyfflD6jZ71L+la/Ux/7AEz/0vtkndjAmMHAV0MnZ7nyaPzkzGTvLbqXfMfpZsDM30zfaKWX/pZxu4yTof8KehUH/7PsrPBM7PGsnJ5jhBZcYnf3B0xQniu+oD8CbiD6f6iCTAjlCMzF1x5lB0FTWl8q0Tiz+mcv9tO1fg5kzYvI43PFRZBIdzzuGV4OVMuyxSH8tApPDNxAbPb3e52xwZm83LkazAG9lzf4D22jDt/FocSSl2f/OQnT8rZu/82Sx5xKYQyvjK1qVWDdPh5Gd5HZh/A7E1vetM0wwytASPkhN8SOpJWnXyFyeoTDvonbO76KjP9hmulqsaD+I14sRaY6bvzSzHDi6MCM3WZ6wJ1bA0Y+oovoJyhpGvCF6B1zrcRH4Tj2VpgZtWBzCo/bRDgtBaY6Seuekm+cZM/2Ytf6aa/nRZghje5UJWuLmld+ly2bwksSv/yGWDHu9JvSVmRm0MAs8ivvEu6yucajcYmE5KscJXx0weiTxJmsSKruPGLW/KvVt4SYOZfgwBuprxoPJPn8LHnZowlrzU6Wn7q8ZznPGcaV2pxAswAc+GjcizyoCFjd5lnj35hewNmCrX3rCF9eRdkDFCNTElw+Uy5EhAKuvSfP0eIosDn4d6XGMrUCpkBl5Ab5K0k2NJckkcEtOcSbEBkNCtLHjl/1QJaxwVm0tX4pFwrCAGV+JZ4V1555e6rv/qrz94B1OJp4rdcvPXRgmVrgls7/5X6t1yd3EppBou4R4mfszstOlv1i7+/afEVr20aAA/PAqjUsZVv/Mn3fPAPGEk+6pP4LTd1LsNt9cibm/DSBU4N/Gz6D7cWX74jI+9b3epWU7uSH/XXRgxXeEnf/Bmtc7/wotev52nw1I3wc391q5VhhU6fL8vAm/Bk3j4jPqRcNEgbwKD++BCe9PKhR5WPj2WbRReoY+k/fw4NNde2Ve2DIXkk/5auSR/TX+XdM+oZnnJNdm9wgxtM6dI3eumFKWNet/l7ZIQ7D6u9a9slwKKVVvp5WI3PpR9ehF+ejYnAkGMyWe0b8WJeZt7Jr7N2pb4Q5i5Ofy2YeCU9eaavrKrHlv+1GflP3OQTfs/LEz4CZskLNiDbjHTosMrtqItjPhl7gh1se4aHyaPnoi2y2otXCwO6pa2Nj9pMmPylRXvGoFpe4uIj+ufho/Z2h6p2NUbhgz7DzW6Q/JjhdRkiQboaOSsRCE8D9AiZE533CAE3fnOX4lN5nU2DzsPz3is/YW95y1um806AGGYCZla2MGmJUd+apQiPC0RGyvKowAzabwkeXpUKNecA1F2YLUx/VO3W654Jz1suObFix5rxAmjKqvGu5Se+1Y1syakTa+CppXHANYMSYFzGb9HZq6Mw51ustJjdkD2dxqAmv95KXMqbD/rojszXFF+tXj2/KNdSQYtvcCkHGO2h/7Tio3dkxHFPlVVnSgT9ZIkJjan33NWHA2DKsPAiA3wZVnvWBkBWTQ+kbvN0/MuyS1q1j/CSfyM+SK8M2+dW2+kShp8wg9LIkFMDdmiJa0WR3FrZok/0n4TN3Xk9vUf+Q4s0ZR4jXZM+I508ekacAEt9gs641rWuNSWJfy+9sNCZdjDwz+sZGeHOw+bvZDJyUOtfOdBfK2feZ5K3uCxaWzarPeGZ/pEJwQte8IIhL/Ei5ZWuSRQdWKuLRYayHi3aSv8y7/Cp9POMzy49nft7TzuZOJT5ls/qQjfq00yAqtUx6cmo+PQ7lyknCmVerWf8iKy24qDBB3WA4DwO/FKbtMsTEFPXpMndf/P4+pX4tZVpaUfGTor/6bZLhRdkhl4rdZs8rhFglmXqfLZOgQbdx40AEZgwq+aOGCH8UMAM0mYdntdYwBEG14R77jdSlkcFZmX8Gp9OApgpN/XU6fAEMFgKzvBOfIe75WPb1UAmH9ZWVvLnuqTPbIyC9G5FwtnFxPfH9TVejGRmDTAjD+S5pNNzBpqasp3HHb3LX/+g8BLXTBrvzL7ix1V/Z03m8RM24oX0xwVmKTN9Om7A4nOf+9yp3xvQa+0UP8pemqQv3eiJ+Elj4OJfAr+SJ56FlwPciA/h1xpgFrnsudEpc3rzHp7EtXWd1Rl+iaeMPOtP3vWX+JVu6OEnj54RJwBsLTBL25XtELrSX7jx67nGlPJy5TJuypmvSALm0pVx8wzMoSt8rrmHAmboBcyy3Vi6/Mt6eBafLqjRyC914oYXpZ9n+dR44RjFKP+UWwIzedLngJndqX0AM8Axspoy524J3jyX4Rkjs5UqzBghT/qzjGu8zFiS+Fxxy/5WpvE8MqcWmFGWGpqiLVHivIIRIIPQPKx8HzFC+KGAWSncaXQdh4CWYbXnADPpauHJL+ERyHKWUaYr45f8yfNJAzO0pY5oL2ltPYuf+pZxAvLkk/rjMV7X4pedM/Uv3ZHMrAFmUWKlMvUcMGKL0bt+UNZx/gxgiZdzkGV4gIey4u+5N4gFzCU+F09GRpzjArOS5+VzJmblAfgyfOmzFVn1nuuI8Oe0AbOS9+Vz+kk54JbhZDw6peRN+nzpl3Rln0tfUU7CS1fchMmrZ6TbFzCLTNaAWWRkzpOs3szTyKtcLU79gK/ISPy4dIQ+yc77qndplF3ydv58CGCW+im/Zct6oDHx5vTlPbqkzDt1LvPCP/op55C9y9ukJ3nV3ORBzvCV4ecdmHEs5LjArNTl5HRu9YGSJm2ScaH0z3P6TPKxSt0726n8nNGUZl5e8o3b6zvCTi0wiyAZRFKZmhthK5VrLd6IEcJPApgRxCjYKLkIbM2NgLTiJpwrfQQpwGSeZxm/xqdDAjNlR7hLusIPtLfoTvyAr1a8hIcf3BYIVv90aPHm/BjJzBpgNi8r7xlozOr5pd4tN9svBg6KtYwX4KGPxN9zD5glTeJz0TEy4uwbmKETva2+PRoIwlOufNSt9Etdy4G1rLfnknfeRyb8WrNiNqch7+kn6I1fXPKr/0TWU8/4Ry/M3bleafWX5JN+J/+eQde+gJm8gAWynvpyAwhqQKsH5sSfp5E/W+bvOTJIDlj9LKuuccPrlnsIYNYqq/Qv61L6t57F74XN83MmDQ/Ks2mt9PyNLXhhoYUcMfLkB+QBZccFZr1yT2NYr+8IO7XALB1CB2oxNoq1drP1PM2IEcL3CcwIHmUWRVYKdRTsXCmWcfIsPWXaihuFyZXGn5/24kcxAyRzHnk/FDALnc7d6IipHzf8QFvqUYaXz+FHja+JV+Yj7xbvUv/Ez3vckczsA5iF5riRe+0Tv7jOpTjLkHeu/mHAcDFj6e9ZXGEG64Q5cGy2m/e5K015FYBw/BgZcfYNzPJhQg2YOW+lbvMvOdN2petDm1Zc/MAfoFaakh/yzn8Hxn/Eh/Brn8DMiqF+gc70X+9lX/EsbA7Myll80pZumUfqyE8+yuWXvMs+h1c9I90+gZnytIU2IaOs5xpITRtEBlKv0pVO+thW3PiXbpnPvKwyXp4PAczmNIzeQ0vPHeUxCu/lLQwfrI4BZvnykr8xBzCzJbgBszO96tQDM7eRtxo8wMxyaytO/HtKJGH7BGZRZrVDvAEiLcBQdoAAkVbcnK1KGgqH4m3Fj1IOX+buoYGZ8uegI/wQlnpwnTlzlqY8exZ+lINEmcazfPL3Tr34qbv4OR8QP+7IHAKY4QUQMeeRepmtCyu/nFQ/dznNrxsp47u3LDwiH/e///2nw9jxi+vLKF8ClfwWtoQX4uwDmJE/QApv8x+gvpImB+UA56tHvKh9gZk2dNYE0HXmMCsi3tnEAcj8F6LLSpWBt2xtVQUvRib82icw8xWkD5FqNm3HFZ4vnFM/h5MNhnmPW6arPc/LTH9KXPn0jHj7BGYp9zS64WnLLeUWz/Z1+P8ovGjRVvofJb9a3DKv2jM51N9YQIxJPO/66QbMzvSqUwnMKGdfV1G8tdlyGhMoEcdXk/FruWeq2/89BDBz6HwuxAEic/BkJjFXgNL6csTXofgyzwuoKMswoBvQevHNNlt8OjQwcxZK2amH8tCqHgbG+HNdQ8F/PqvHD6spNX4YnEp+yKcVHx2+mhG/xo++tKz/KjN8oLCAAVcKBIygi5+w8MRHMHNgJswXby4jFZ8M8QMsADl+SR9XfP1LecJZ7UIx1gAhOkdGnH0AM/lYGSQLc1sOcOIJ5+7Dpszww+ARfpXuiA/iomefwKwsf+nziCdL82nFk3/PSLcBszOyWcotnl2swIxuUnd9y0Q4hiwBZg7Yb8DsDFdWAzNM1Qm5QJQBwSWkEUYNMTLSllY+BiCDh8G3DCufxWE1aulfe15Cgz+0dQDRpa6EB4Dx7nZkeY5MqcSyYlYOrMLVJzf/Z6sg6ShzQGTu773mnzKWxFeucxfySdvU+IQWdRdGsTKJ7y+Q3EXky5SeqeUrD9sjgFMGPTQBFGjieg8vuNm6mQMzX1XioTRWjGIB3WzllPm04tvmET/1m9Pdq6MwWyvosI2onVk848oTDfM8a+/izkFI3kvasoJY5pF6KhOosHJmVcxzQFYZP8/ipwwuYJKwmjvihTR3uMMdpi+R9PmsuqFfu9byvBD9lvBBnZ2HMuHIil7aSdjIJG7LHfFNOuW07L7ao1cPNKSfk0NX7XzhF37hJAfkY1QH4a36l/5L8unFKfOqPePVyNbSlX7hNz+0qL+PDVxA6m/Ryrit5xENS8Jbee/LvyVv8ScP9IL6kwk6KBNJq/WAmT6DR/y5TAB+4vba8yTClvBrREev7whzg4P/73Xdjnob4/AM70reNK/LQCQGI0QDuD37K77iK86Wy29k5pVw5xTAZeCch+U94E28+PXcEQ3qQZm6lwpaJej+zNy7u5mEj0xZvnob9IGKMFIeJRDxXqYpgUjpn3T5CyINxAI08i/jehYfyJMf0CZuyq3Fn6dXT37SMXgtT7OcL/3SLz3vPwjnaXvveAIwoIUFali0znkhH/HRwJ3nK74wackJ24or7VHjSzMyrhfwrwOucyAv2hmtzk8oT784CaOsnj0JGpTxnd/5ndNfqgSU8UubnBQNp6EcA4m/uSIb/uaNbESGtdPIzGX9qO+RRfLYsujp2SVl9mROmPz1AfrDTsDnfu7nnh2M+aOzZ+UxomPEyxGNozLQh9aWVcdeHYRpA65+IR/v/t/Zivazn/3sKazXFkvCWvTFf5QH+ka8HoWrF+DQsoBZwtBDLgAONAKqzvu5lzK0iKNMLj9x4zeipRc+kgllrLGhv0fDSG4dJXjwgx887RrJB39MuOkWfIg5ODBzIVvOfzgE6EwIl5+zIqlk4vh6bX5uRMMn3txNRVquxtonMFO+xgUYHMgvgUhWuOY0ip+BbB6GvhoQmccr3/FDmtKW4a1nPBImHbMvYFaWF9pGirFMc9LPLVmJ/wbMwokz7gbMzvDh0MBMn6H8W1Z4z+hHQELP0kXyadnRwGWQjt7BDyuyn/d5nzetohmchYkT4FBzR2UsCa/lW/ot4dVI77R4FH+rQepswoYX6m2889HaM57xjC4PSloP+YyXo3r2ZErYKL1wPAlwSft5t9LvD9jvd7/7nV0hM0YIU29xyav3nkkZ4f1xXG1kzGtZ7dfLF42pW8sVp2c/8pGP7B7ykIdMwEw8u4IsHqAr5uDAbEmjromTirRcjN43MCvpvRCASOjFI8+HBGYp6zS7LVmJ/wbMwokz7gbMzvDhNACzUb86v+Wu/jZKL7xnhBtQABK6lS65znWuM/kJi1/AW801AOHlGruETnEOaa0WZqUog7o6GXitEhls7Ua0rAF5DQ+WpEVDC0TEfwQMtWnP4LG85JNnMuLdcQqrh/7OMcAj+YVn3ntgRlho7bmjPEayEJpb/DDWt0Bd/Edtkq1M/+AQ2dFGeQ6fN2A2EDqMGjXohRKeumzALOJfdzdgdj5fNmB2hh+U7jW5lblkABsNTr2BTdgovXADKrBh68Wq0ed//udPq0YGF3nQhz2zD305ohOveuUs4WWvDsKsBqkzgOYeR89Wz6yY2e4OL3p0LKkHWnu2lwcw0QKG8deGPau9R0Zd1Z9RX+/SubfR31Pd8573nFaG+AlDM74BQZ6lBVBa1pgVemsukBtw1HKV0bPKHgGrFn1L/S0SkQ3n3tGJF2zAYPi8AbMNmE0Cv+aMWU/xnMawCH/L3YDZ+ZzZgNkZfhwamJ3P9fpbrz8ZvEcDBOCQ7ZOaawDs5WFgM9hLC4w4W/pZn/VZ07OBxiDbo1FYD2QkbJRHb4AVZrBLXodylRE6PeML152OVokCOlrASdwer/cRhhet8uMfUNBy1avHb+Hkylmp0AzoAV6uyPER1V3ucpfpyhdfjjvyY8vXF+M+PANwfcglfsvWwNjcr5U2/lbvPv7xjzetj75yl17Ndc7e8as11keUjj+pu/5CNtMntEfMBsw2YLYBs/SGq9wNmJ3PkA2YneHHoYFZBvlDu+e37vlvGSRaYMbgYdUjNFo1y5+Y88tg33OlN5j3rDg926Iv/kBPC2jwl3dARM3V1s7P9aw4WckxyAIXAKtrfKwSAQ74c01aNJVfadeer7zyyl3P+o9Vf7rdsoCKK3p8aWhF2Ydont1T6Hqg5zznOdOKmWfAhD/g47+lxWOvuOKK6Y5OX+DXrDPdz3/+85tWODDcs5dffvmuZ11b5KaGln3Na14zXeHlGq+WVb+eDY8AUnIXedVfPOtDzAbMNmC2AbPzx6bp69Ttq8xzTNmA2RleHBqYLQELo0G+BjJKP3XoWUCjV4aVEash4gEjVkmcMbOiIoyVf1nm/Fm6kZ2nmb/bIutZNwAACS1rdcRF5i0rvVWNngVUHGw3oNuaeuELX7h79atfPd2f6EooH7Q99alP7dqnPe1pu0NaZ91csrzGvva1r53+Pcd9oDWbC5JL0OVZXCAMT3zFbLUKgMNzK2fS4a82smrW204FeHsyQx5HFvDpmUw2em4vvbBeWmFZHUwfyQTCJOVIwExkifdxXcaI6OOEjxiFfvd8za/LcJ2D6zIg1ZE5Dl2nMY164gcBZgi6dzM7W5lukj+NdO+bplF7Z8XMZbeZXesDBh38MoAe2qizsnr20DTIHx33vve9pxktZYIehgzhyb7b5jj59XiUsN4KTsLUp2e1v38uANrpjqz4lDLSS99bwRGmH9oebFlAxF2DLWvV481vfnPXvvKVr5xWKqxW1Kx6ueC7Za1sWJXgun6Ibv3sz/7sqUyrRMLcW+VS45bNX/S4dLRl8bhnldGzVlf8yX3LAgpWQFoWGHHvZc8aZAEQY6Ptsg984ANn/93ClUz6S227OH4A8EgmevKUsF4eZLQHaISN+txowqB85ZBfz+hSR2Cd0b+sPDL6UPSn52yR4kX4UnMB89S35i4Zx9PPWy4+9IzwHq+FtfKOvzrjlTqQj/BWO4gTGoYrZjKRGaG77nWvOyWk7GS01iAEYS2roiMzEirpdRyzEjfOo9tyrlmOTgmlL8ljRMeFEE4YKHX89myf37Pl7mtf+9rTTCYDWc2N0ByyrsqNEB/KHdUDjwwe/sbIzJoc6gPpPBTHiDYKZz7LL9/1q7WdvNZGpd9IrsWtKbnSD0iwtG+AM9ON8sEPsuMeHpeMtqwzSB/72MdWWYOcdmhZWyStrQX++nkLaMTfNT35f8WaS3+QiZYFMFyiucYqt7cVY0XGFT3aA3DwZZeLbgEkgAyIqJ2NKf2AN6sVLeuvnmrbXfFzTxd90bNkn3y3rL4zks1D6pgt740Dp50DTWAWwnUiHc1M8Uu+5EsmRa5TUcqtjhd/cXqWki8HgdrzqAPLo1cG+ikul7o5dCeuZWoKlKKD1C3H96zDij1rtjRaRu1tDwjrLeMK0wY1/pR+I7CQuNpWXIMu/hqgb3azm018UU7L4l0PTAgvwUfteUQjeg5t0NVrL2ACcHdWBKjADwMSGVFHg1QvvTDx5dOyQI4+1bLvfe97q9sG5VaC7ZOeBTp6A727lkZAwkrzt33bt+1uc5vbTBcb4wmQ4q5Bq862SHIHYc1Fg9WJnrVK07O2QlorG/wBM/cD9Wxryyr+Vj9MVFo2F0G29ITVgvSv47r6YU/fkT2yZYJgtk0u+SlPv5J+ZMi+9C0rXJ4tS7e39EP8W2njj9ZePU9CB4z4tIVvHLgmOdAEZjqHjq4T6YxmXV/8xV88DU4n1XGUE5DXcqOQ0Fqz8rDPbUZrdkmJmS06kGjmCWjU0pV+8lhjy7xaz2vyT9qeIIlDmRuAGErUoMQP8LvTne40rXr08qC0DUAt60Cje1p61vZJb5DWLoc8cyFvgKS2KhI/WySAPJ44Q/LiF794Winhb7sGmOkBHmEjQGILJGczai6w0Tpsu9TfBMQKSMuShQyWPReAB0zIjP5iUM9WhUlJa+uNP9myutazta2L0k/f700IyHBv4oPeVr9b6p8+1nLpoQCT47rq0QJM/PFB+T3Toq/076XfR9gImOJ5SU/teR90bHlsHLhQOdAEZiqkw+hElI4vL25xi1tMX1xQuDpfT5kvCaOISgU8f6Zsa5229KOwekrZyoVtmEsvvXQCYw4b2t7wB9cGWlu0mTW33N5MXNjoqxXA0FmMlvWlhr//6VnnNVrbKPHvHTR1XsN/uD384Q+f/sfN1g0eWKmwknjJJZfsHv3oR5/9O6X8rVLpWi3x9UvLWjHpreAIsxKEXy0LNPcO9e4jjJyRvZ51JkJZZMtAa6WiBBlAas9aWQF8WtYKLNlsWel6+S8J0wd7g6SBvtd30v+AIjqAkR9/QEv60SC7BPiU/bn2PFKutTRzv1Ee9EhvFZSs9AAXXi+pay+OPPD0uBZ9PWAnTDvOeVO+o68nM5GDHj97dUxYWWbtuZf/FrZx4DOdA11gpoMaALhm35dddtkELgyqtnMAjjXWSkE+l625/i/RCkrP+rS2BRT454CrLRcAzdkMWyNAhO2q0TaJrRJn03rW+Q4Xx7UsQGYFpGXxsDWAxx8oaK1ULfG3sgFo2KoBTAys/LINK2xURtL1Vj9GYb3BTdhxB6WjpBsNwugwSJuAyBcwwSd1MzDNJxC194AZ8Q9lDXK1QS1+6tmTDXXMQNlyKcDkl+fUh790ea+5+DACkSOZwHuy2bLyD401F42jiWKr/qV/rX7xE69W9r79SnpqeZfhtefQ23Lxqdde2qqWb+lXo+uofp/pA+9Wv40DPQ50gZkOauUAMDOztxUIlAEg7iqpbcGUfi0gEn9bMlZQWtanta1tmPhnu6SltG2v2YYxeHKd+eFnkFU39eodZBXWyjv+8hrNVHurM/jcUpTxp9jWGIoTnVGQVj2Ua3BGu2dxEl5zR4MspV1LV/qNBkj1LeMf4rkcRGrPyuRP7sMTdHlm0iY9V3v3ZAIf1tZtJA+pg3rULNA5WjHTv/QBAE8fCtAjS5HbHh3hJVqOa3t8TlitfvETZ1R2rw5LwpTVa+99hGmv0uCtuqWe3JFZInMjXtEDPauMnllCQy/9FrZx4DOdA11gRplYsdH5KWVAxoqL6wRsxXjv2RHgkWcPsAjrKQBhBgj5tKyBRRx1AELUB13SAhJm46Viqz2PFAmF2auHAWy0KlArt/RDe6uOS/zDA3kyXHQDCAZb79pbOS0rfk9p4/GovXrpheFTq/x9+aOxRwdeJA439Va/ANheemHirrHyGJmRXC4ZIEc0qjt+sOKmfb2jkdz3wB2ZkkfPLukbPX6P6iB8xKtA1WlIAAABzElEQVTUseWqd29SIXwJHWviKAOvyCC+6w/6dcAyt6eHhI3kasQn6Vs8iv+h5XaU/xa+ceBC50AXmOn4trgoJABGp6RgKQBKoqcsl4b1FEHK6yl1dEQh1NwoTOVQivLil3d1896zPRqFoXOkcGu0lX6jMsq4x3lWvyhmbYne0G5gleeSOvT4JI9RPaTvDXBL6BjRuTacjBgA1QWt+gGDNquk4V2vriMayEwvvTDl9ezaMtDQa09h6BAPGMAHfEETwOUcHZka0Sj9Gjvi05LwkaJeQ1/SLqGjFyf5LHHT9nPex7/lkueePpVfj8YlYSNe7yOPURlb+MaBC5kDXWCmc1PEFAUlzehU/E/CKGukpNbScRJlhG89hbS2HqP0ZbtRzt5jtGf5Hv+5K06vPZbk0UsvbEkec7qO+q6Mng2N8vUceZdmzrtW2b38E9ZKG//EW+Mmr5or39S15UonHh4YtCMrnumG8KaW/+Z3NA4saeej5Xj12K12jj8aNrNxYOPANcuBLjC7ZknbSt84sHFg48DGgY0DGwc2DlxcHNiA2cXV3lttNw5sHNg4sHFg48DGgVPMgQ2YneLG2UjbOLBxYOPAxoGNAxsHLi4O/H9q1LOsnBYbfQAAAABJRU5ErkJggg==[/img][br][/b]
Plot the ordered pairs that correspond to diver's height and time. (Use the Point tool or input the ordered pairs)
[b][size=100][size=150]What is her rate of change (speed) during the first 0.2 seconds of her jump?[br][/size][/size][/b][i]Use the Line and Slope tools or write an equation. Then write your solution below.[/i]
[b][size=150]How fast is she going during the NEXT 0.2 seconds?[br][/size][/b][i][i]Use the Line and Slope tools or write an equation. Then write your solution below.[/i][/i]
[b][size=150]About what time does she reach the top of her jump? Explain your reasoning.[br][/size][/b][i]Hint: What will be her speed at that time?[/i]
Now the points are plotted for you. Use the line tool to connect the points.
[b][size=150]Now use the graph to estimate what time she hits the surface of the water.[br][/size][/b][i]Hint: What will be her height at that time?[/i]
[b][size=150]Use your estimate to determine how fast she is moving when she hits the water.[br][/size][/b][i][i]Use the Line and Slope tools or write an equation. Then write your solution below.[/i][/i]
Move the sliders for a, b, and c to find a quadratic equation that matches the graphed points.
[size=150][b]Since the diver's height (h) is a function of time (t), we can model her motion with the basic quadratic equation: [color=#ff7700]h(t)=at[/color][/b][sup][color=#ff7700]2[/color][/sup][b][color=#ff7700]+bt+c[br][/color]Based on the values you found for a, b, and c in your graph, what is the equation that fits her motion? Write your equation below.[br][/b][/size][i][size=85]Remember, you can right click on the orange line to display your equation.[/size][/i]
[size=150][b]Now use your equation and find:[br][/b][/size]a) the time she reaches the top of her jump[br]b) the time she hits the water[br]c) her speed as she hits the water
[b][size=150]Describe how your estimated answers above compare with the results the equation gave you.[/size][/b]
Close

Information: Investigating a Quadratic Relationship