IM Alg2.2.10 Lesson: Multiplicity

What do you notice? What do you wonder?
[table][tr][td][math]y=(x-3)^2[/math][/td][td][math]y=\left(x+1\right)\left(x-3\right)^2[/math][/td][/tr][tr][td][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASYAAAEgCAYAAAAZnd7HAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFiUAABYlAUlSJPAAABkrSURBVHhe7d1/iBXV/8fx2a/2yaWyLAqEyl2yHwiRYoFCtbspFf2T9oMgIt3+LKH6U0NWCau/+oFB/hHsCv2kH2oFWRnrUmQpWGQ/oIx107IfoGV/RFje733NnrOOd+/dvXvPmXvPzDwfMOydWXecvTP3Ne9z5sxsW6ksAoCA/J/5CgDByGwwHT9+PNq+fXt04MABs6S5WvX/orj27dsXDQ0Nmbl8y2wwnXbaadGmTZui5cuXmyXNNTAwYF4BzXH99ddHW7ZsMXP5lumm3LJly6IvvvjCS/XS09MTT5U6Ozuj3t5eM3fS5s2bo507d5o5IF06Ef7xxx/RypUrzZJ8y3wwydatW+OvLrq6usyrk3QwKPT6+/vNklEKJC1fvXq1WQKkS8f4nDlzovnz55sl+ZbpYDrnnHOiW2+9NXrmmWfMksZ1dHSMq7zWr18f9fX1mbmTVC0J/UxoBlVK27ZtK0y1JJkOJlHVpIBQk85FZTCtW7fulK9JO3bsiL/+8ssvNOeQOtsiIJgyRMF09tlnO3dGK5jEBk2taknfP3TokJmLaM4hdQqmq666auwYLYLMB5OacwonlboukjtdVVJ3d3fVM5Rtxlk055AmHV9Fa8ZJ5oNJfDXnFEZaT61qSWwzzqI5hzTZZpy90FMUubklxVZOLk06DQuwFdDg4GD8NUkBZIcUaBzVhRdeGA0PD0eLFi2Kdu3aFS8HfFqwYEHcVVG0k18uKibx0ZzT5VgdALWqJduMU2hNmzYtuv322+MqK9nnBPhiWwFFa8ZJboLpoYceii+ruoxp0nB/HQQKm2oUWgol+/1Zs2bFY5yWLl1Kcw7e2eq/aM04yU0waeCZKp5Gm3IKlomqJX1PIVQZWuo0r/UzgAtV6Bqnp26KoslNMImqHTXnVDnVS0Gmq3DqO1I1VOuSrAKpViWln6n1PaAR9larIjbjJHfBJPU257Tj7d3a6sQmXBCKp59+Ou70LmIzTnL3oDg16dT3U+2qmk/t7e3R2rVrozVr1pglgD86htWMcx04nFW5qphEneDqD7KX/YGsUcWv7ggdy0WVu2CypW9RzzTIPh27RXqSQDW5Cyb7xIHKW0eALCjikwSqyV0wiXaqHZwGZImt9AmmHFJzTlc0dGUDyBJV+npoYZGeJFBNLoNJdMZxvUUFaKYi34JSKdfBpPY6neDIiqKPXUrKbTDpioYeruVy7xzQTKrwFUpFvAWlUm6DSWxzjjFNCJ1OoDpOacaNyn0wCc05hM6OXeK2qFG5DibGNCELGLs0Xq6DSbSzVSLzvCSEirFL4+U+mNSZ6PKcJiBt9rlLRR+7lJT7YBKFk0rlqTynCWgGjVvSxBCBUxUimHw8dhdIgx27RDPuVIUIJpXIGubv40+JA77Q6V1bIYJJtPNt2QyEwD53iWAar1DBxI29CIk6vXV3QpGfu1RLYYJJbCc40Gp2CEuRn1I5kUIFk+0EZ+gAWo0bdidWqGCyN/YyEhytpmNQocQNu9UVKpjE/rECOsHRKqrYVbnTjKutcMGksxSd4GglOr0nV7hgUumsK3SMBEcr0Oldn8IFk9hOcEaCo9n05+jp9J5cIYOJkeBoBZ0M7UhvOr0nVshgEjsSnMehoFnsSG+acZMrdDCppGZME5pFFTp/mqk+hQ0m0ZlLV0joBEfa7BAVnRAxuUIHkz1IqJqQNh1jemAhwVSfQgeTSmo9OZBOcKRJQwRUmRNK9St0MImaczpwGDqAtNiKnE7v+hU+mPTnclRiUzUhLTq2VqxYwRCBKSh8MIkGvalzUpUT4JO9L45m3NQQTGX2/jkFFOCTvS+OP2Q5NQRTGffPIQ2qwrkvrjEEk6GDR6HEUwfgC0MEGkcwGRo6oA5Kld6AK4YIuCGYEnQQ6YBiwCVcMUTADcGUoA5KHr0LV+oSYIiAG4Kpgs5wttMSaIR9igBXeRtHMFVQc04dlnSCo1Hr16+Pb3XiKQKNI5iqUNWkoQMMuMRUqW9Jxw19S24IpipUNTHgEo1gQKUfBFMVDLhEIxhQ6Q/BVIMOLgZcYirUt8SASj8IphrsgEtd9qVqwmTUr6Rqiea/HwTTBHSQKZQYcInJ6FjhzzL5k+tg6u3trToeSWc3fa+npyc+oGpdfeMJl6iHjh91eqv5z4BKP3IZTDpQFDq2MzJJ3+vs7Iz/WkVfX180MjIS9w3UooNNP0PVhFpstUSntz+5DCaFkkKn2iVbBYyWq4NSX/v7++PwqlU16d8oxCYKLxSXmvq6eku15Fcug2l4eLjmOBJVSAqaJP3biSoi29yjakIlXbVVOHElzq/CdX4rYCpvFdAlXgVWLTNnzowWLlwYPfLII9HevXvjqVQqRT///PPYvJ1QHAoke7Mut5/4VbhgasSRI0eixYsXx0H06quvxn+48MSJE9Hhw4fj18kJxWGrJVXU8KtwwVTrzKaqqZalS5dGGzdujP/N7t27o/vuuy+aNm1aXEXpdXJCMVAtpatwwaRwGRoaMnOjKudr0Zmx2pU+FA/VUroKF0zq6E5ehbNBU88Bpg5OBRtX6IqNail9hQwmHVAaUqDxTPo6ODhovjs5WzWpjwnFRLWUvraSLi8VVLUrdPXQzxw8eDB69NFHozVr1pilKAIFkk5ouiOA4SPpKfRVuUbLcJ0pVTFpvBSKhWqpOQpdMbnQVTndhqChBCgGqqXmKXTF5GL69OnR0aNHOUALhGqpeaiYGtTe3h7Nnj07HgFOky7/qJaai4rJwZIlS7iHriB0k65OQqqakD6CyYF9fArjmvJNJx+et9RcBJMjnUF14NLvkF/atzxvqbkIJkfz58/n2eA5psG0VEvNRzB5oDOqQon+h/yxf/mEiri5CCYPNFBTT8zUQWzvwUP2TeU+SvhFMHmiUp+/3psv+oMV+qu6PJ2y+QgmT9T/oHBSf4TOssg2DQFR9UvzvDUIJo9ULfFYlOxTf+HDDz8cD6as9ex4pItg8kxnWFVMDLrMLu1DLma0FsHkmf4Sqx10yfCB7FHzTftOFzN4CFzrEEwp0JmW/olsUoc3gylbj2BKgQZdPvjggwwfyBg7PEAnFAZTthbBlBJ1hOvMqzMwwqdmt/aVmuEMD2g9giklOuPqzKsz8NatW81ShIrmd1gIphTpzKszsC490xEeLtvhrea3muFoPYIpZfZMzIjwcNkOb/ZROAimlOkMrEvPevoAf0I8PBpvZsed0eEdDoKpCXTpWSPC6QgPix3hrea2xp8hHARTE+hMrDOyKiY6V8OhE4Uel8so/fAQTE1i/wKw+jEY29R6ulKqSfuDEd7hIZiayFZLNOlaKzlmiRHeYSKYmsg26ezoYrSGqiSacGEjmJpMnax6nAa3q7SGmm+6QkoTLmwEUwvoTK0z9vLly80SNANNuOwgmFpATTqduXWVjkF9zcNVuOwgmFpEV+nsEwgYeJk+9enpZKCvNOHCRzC1kKolPexeTTrupUuPgl8nAPXt8eSAbCCYWshepTt69ChDCFKk91b3wtGEyw6CqcV0L50qJzUz+OD4p1BSxaT3l3vhsoNgCoCuEGlUuP0QwQ8FvaannnqKx5lkDMEUCHXK0t/kjwLe/gkmhgZkD8EUCPqb/LHjlehXyi6CKSBqbtjL2pzlG6dQGh4epl8pwwimwOhytsY36bYJzvZTp0C345XoV8ougilA+lCpb0R9JHSG109BrkDXE0MZr5RtBFOg9CHTUy97enq42bcOCnA14ewzr5BtBFOg1Deix6PYm325UlebQkkBrquaqjaRfQRTwGw4qSNXHzzCaTy9J3pvVF3qvaKzOx8IpsCpA1cfONtUwUk2lOwTAwil/CCYMkDh1N/fH19tIpxG2VBSNang5gpcvhBMGaGrTAonVQZFDydCKf8IpgwhnAiloiCYMqbI4UQoFQfBlEHJcNIHVR/YvCOUioVgyigbTp9//nnuw0lXJDs7OwmlAiGYMkzhpA+qPrALFizI5e0ruhKp4LXjlAilYiCYMk4fVH1g9YgPfYD1Qc4L3femUe+EUvEQTDlgw8k+aE4P3s8yNUvVsW+f7KlKkMGTxUIw5YS9fUWPTNFNrKqesnjzr0JIzVJ17NsOfhQPwZQzuol1y5Ytcae4PuBZatqp0tM2q1mq7VcfGoqJYMqhZcuWxdWSbdppCrl6slWSKj1VfPQngWDKKdu0U3NocHAw/uCH1vekviQ9DE/bpmedaztV8dGfBKdgeumll6Jjx46ZOT+0zt9//93M+aF1Hjx40MyFS9u5b98+M+fH//73v+jNN9+Mn4ipikTjgTZv3my+25hXXnkl+vjjj83c1CmQFJLaFgWnnji5YcOG6N9//zX/wo/t27dH77zzjpnzQ2H/+uuvmzk/du3aFe97n9QU9r3Ob7/91vs6a3EKpq+++sq88uf77783r/zJQijJX3/9ZV75c/z48eiss86KO5F1sOrSu/pubEA1c2BmMpAUkgpLNeP0+owzzjD/qpj06Bbf/v77b/PKH1W2k1G3gWvXAU25ArHDCtRkSgZU2s8W1/+py/+zZs0aCyQNClVYdnR0mH+FPNFVYU3a942EFMFUQN3d3fEBo3BQSKg5pX4eG1JDQ0PmXzZGldG2bdvidWmdOkAVhmqyEUj5p32r/a1A0r63x8BUQqqtXEI2XEOuWrUquv/++6MzzzzTLHGnzs977703Ovfcc80Sd88991x8pWr27NlmibvLLrssvoL0wAMPmCXuXnzxxWjhwoXRFVdcYZa4U3/IpZdeGl+hq0X9hO+99170/vvvx/0dtkm5ePHiaN68edHMmTOjRYsWxcvkk08+ic4777zo8ssvj+f1899880106NCh6Ouvv45fi5qQN910U3TjjTfGXyei/1/NuWuvvdYscaeAVb/VkiVLzBJ3n376aXTkyJHolltuMUvc7d27N/rxxx/jY9QX7Qd1tdx1111mibv9+/fH+16fz3roeLjjjjuiw4cPmyWjdGLUSUoBVvMEpWBq1M0336xQY2JiYmpoKoeUSZNTOVVMt912WzxGpr293Sxx99prr8VnV52lfdEgw+uuuy4+y/ty9913R3feeWf8+/vywQcfxFXIxRdfbJa4U/l80UUXRZdccolZ0hhdKf3tt9/i1zoTa//Y7bzgggui888/P37dqD179kQzZsyIrrzySrPEnfrN/vvvv7gK9UWViCrKZAXp6rvvvot+/fXX+Bj1RU1mTTfccINZ4u6nn36KrxqXCxKzZGI6ZtQC0u9XSf2btmqqKo6nBq1evbr0559/mjk/1q1bVyp/AMycH0888USpXCqbOT/KH6LShg0bzJwfmzZtKn355Zdmzo+BgYHS7t27zZwfL7/8cumjjz4yc35s2bKlVA5mM+fHu+++W3r77bfNnB+Dg4Ol8snTzPlRbh6VXnjhBTPnR7l5WHr++efNnB/lJnrp2WefNXMTK4diqRzep1RH5TCK37960PkNwCt1cOsqrPrjVBmpI7ycNfFFFvUv1YNgAuCNQkndB2qmTTWMkpyCyWc/kHX66aebVwCyRn1GqpIaCaMkp87vIlOH/9q1a6M1a9aYJQBqURWlOw1UQVkaz6YhHcllFk05AKlTJZUcYKnX6ofSgwCrIZgApE7BpOad7pW0I8LVKV6ryUcwAWgKVUdqvimU1Dk+UT8UwQSgKWwQqXrSzdwTIZgANIUqpcq+plqcgsmWZcm7h13ZTjGf67SU0lp3qLRtk51J6pXG+6j9nVyn5n3SNmrdkx20k7HHZXLyta3299fksk7bz1Jtct1Xyd9fx5Pr+ylaT3K/T3Wddjt0m4zCadL3TsMFGqEh5xpirq+ioebl/3BsvhF2nXbYuo91in6+XEaOTT74vCUluX36/V2l8T6msc4krUfr87HOvr6+sW21kw/aP1q33T7X7Uxun6b+/v741g2X9Wo9yfdQ26vJhX5e67Tbqfd2KuvUz+j30lfRz072ezrdK1dJG6w31ycf69QbYd/UEIPJbp9+T/2+aUhr3/jaXvuh9xVMmnzS+nwdO7X4+D+0P5K/u95Lh/ojpn1S+X7Wu58qQ8nSz090PHrrY1KZpvKs/B+aJX5ova6lqMrI8g53Xk9a7Palycf7WEn7W0/CdGXLer0PPoyMjHg/DjUQsPzhNHPp0KX08ofVzDWmq6srHsho97XW6WO7y4FnXo3S+1vP8aTjupwz447vcqiNW2eSczCpza1Jbc9yKnr9gNkPk68Dtqh8vo9ah+1n0YfIdZ3aLn14dOz4YtfZ1tYWb6e2V8tcqN9H67D9Sz76gpL0PurD7hqo+rDrsrzdRnHdR/pMJ/uE9Hvb9yMtdQeT7hROTpYSWmdNvaHJpK5HrXWK1qM3dqpnkInWWUSNvo+1aD/b/a0qwvXDqdDwtW2WQk5nZJ2ptW69B/p/XOn31Xo16cOv8PNFnx0flY1+V22nAkr7SPOu+0jbpXXqONL7qN9bYeUaohOKG3R1uOaaa8amN954wyw9ldq3muqVXGc5kc3S0XZx+RdvqE8kuc6NGzeapaO0Pq3XhzSex6Ttm8r7NxmX97Ee6ndweT/18/p91f9gJx2S9rUvdr16PxpV/hCO+/lqyxqh7dO6fND+0Ptqad+7/u6WttOux9c6a/Ha+a03xPUN1i+b1oepSMGU5vto6f9w2d822JKT1qfJ53ZrO6dwDq5K25QMS7tOHwGq3zsZJi6qBUbltrvyGaS1NLy3kukpdmNd3mCtTztJB6VeJycfihJM9n3UvvD1Plb7ef0fPis80THksp2SPDb1Vdvout/tSdeu18670vp8fsjtZ9Bup44pn+vXe6vw83niqKbhYLK/sDbSfnU9SLVOrafa5IPWX4RgSuN9tCcercPX/q5G67YfqkZpH2s9vrfThpFdp94TV1qP1uuLDWL7+/vYTrvvfa2vHjyPqUE8jyl86vgtf5jMHLKEe+WQW4RSdhFMAIJDMAEIDsEEIDgEE4DgEEwAgkMwAQgOwQQgOAQTgOAQTACCQzABCA7BBCA4BBOA4BBMAIJDMAEIDsEEIDgEE4DgEEwAgkMwAQgOwQQgOAQTgOAQTACCQzABCA7BBCA4BBOA4BBMAIJDMAEIDsEEIDgEE4DgEEwAgkMwAQgOwQQgOAQTgOAQTACCQzABCA7BBCA4BBOA4BBMAIJDMAEIDsEEIDgEE4Dg5DaYDhw4EPX29kYDAwNmyUk7d+6Menp6ora2tvir/i2AcOQymBQ8nZ2dceBUho7mFUZ9fX1RqVSKurq64nkA4chlMK1fvz4aHByMOjo6zJKTVEGtXLky6u7ujufXrVsXf1WYAQhDLoNJoWSDp9LIyEg0Z84cMzdK/5ZgAsJRuM5vNeUqKykFlQKrlg8//HDcdOLEieiHH34YtxyAu0wH0/DwcPTZZ5+NTfv37zff8Ut9UceOHTtl0rJ//vln3HIA7jJfMa1atWpsqke1fiepbN4lLV26NFq+fPkp07Rp06J58+aNWw7AXaaDSVfe9uzZMzbNnTvXfKc2BdDQ0JCZG1U5D6C1CtfHpCty6ui2wwjsa3t1DkDrFS6Y1JTr7++Pxy6p4tIgTM0DCEdbSb24BVXtCl292tvbo7Vr10Zr1qwxSwD4UriKKanRUAKQrkIHE4AwEUwAgkMwAQgOwQQgOAQTgOAQTACCQzABCA7BBCA4BBOA4BBMAIJDMAEIDsEEIDgEE4DgEEwAgkMwAQgOwQQgOAQTgOAQTACCQzABCA7BBCA4BBOA4BBMAIJDMAEIDsEEIDgEk4O2tjbzCoBPBJODAv91dSBVBJMDKiYgHQSTAyomIB0EkwMqJiAdBJMDKiYgHQSTAyomIB0EkwMqJiAdBJMDKiYgHQSTAyomIB0EkwMqJiAdBJMDKiYgHQSTAyomIB0EkwMqJiAdBJMDKiYgHQSTAyomIB0EkwMqJiAdBJMDKiYgHQSTAyomIB0EkwMqJiAdBJMDKiYgHQSTAyomIB0EkwMqJiAdBJMDKiYgHQSTAyomIB0EkwMqJiAdBJMDKiYgHQSTAyomIB0EkwMqJiAdBJMDKiYgHQSTAyomIB0EkwMqJiAduQ2mgYGBaN26ddGBAwfMklPZ7+/cudMsARCK3AWTgqizszMaGhqK53t6euIAStKyzZs3x697e3vHfb9eNOWAlJSbI7kzODhoXo3q6OgoDQ8Px6/1VfOWnbffr9eMGTNKjz32mJkD4FMum3Ld3d3m1ahy8Iw16dSEW7FiRfxa9D39e5p0QDhy3/mtQNJkw0pNPIVRJdv0q+bEiRPjpomWA3DTprLJvM4l9Sd1dXWN9SNpXhXTypUr43nR90ZGRqL+/n6z5FQ7duyI3nrrLTM3as+ePXEf09VXX22WRNH06dOjJ5980swBaFSmg2l4eDi65557zFwUd2jPnTvXzI2GkKqjZODUCqbkVwCtlfmm3OOPPz42JVULJUn2N1mqlgCEI5dNuVqhJOrkXr9+ffw9G1IaXqDqS/MAWi93waTmmIIn2VSTOXPmjDXVNHZJgaS+J9sZXqt/CUDz5S6YVBFVNtVE4ZMcRqB/p0nLK0MMQGvl/qocgOzJ/TgmANlDMAEIDsEEIDgEE4DgEEwAAhNF/w+GawPqkY/wlQAAAABJRU5ErkJggg==[/img][/td][td][img]data:image/png;base64,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[/img][/td][/tr][tr][td][math]y=(x-3)^3[/math][/td][td][math]y=(x-6)(x-3)^2[/math][/td][/tr][tr][td][img]data:image/png;base64,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[/img][br][/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table]
For polynomial A:
[math]A(x)=(x+2)(x-2)(x-8)[/math][br][size=150]Write the degree, all zeros, and complete the sentence about the end behavior.[/size][br][br]Degree:                     Zeros: [br]End behavior: As x gets larger and larger in the negative direction,
Sketch a possible graph.
Check your sketch.
For polynomial B:
[math]B(x)=\text{-}(x+2)(x-2)^2[/math][br][size=150]Write the degree, all zeros, and complete the sentence about the end behavior.[/size][br][br]Degree:                     Zeros: [br]End behavior: As x gets larger and larger in the negative direction,
Sketch a possible graph.
Check your sketch.
For polynomial C:
[math]C(x)=(x+6)(x+2)^2[/math][br][size=150]Write the degree, all zeros, and complete the sentence about the end behavior.[/size][br][br]Degree:                     Zeros: [br]End behavior: As x gets larger and larger in the negative direction,
Sketch a possible graph.
Check your sketch.
For polynomial D:
[math]D(x)=\text{-}(x+6)^2(x+2)[/math][br][size=150]Write the degree, all zeros, and complete the sentence about the end behavior.[/size][br][br]Degree:                     Zeros: [br]End behavior: As x gets larger and larger in the negative direction,
Sketch a possible graph.
Check your sketch.
For polynomial E:
[size=150][math]E(x)=(x+4)(x-2)^3[/math][br]Write the degree, all zeros, and complete the sentence about the end behavior.[/size][br][br]Degree:                     Zeros: [br]End behavior: As x gets larger and larger in the negative direction,
Sketch a possible graph.
Check your sketch.
For polynomial F:
[size=150][math]F(x)=x^3(x+4)(x-3)^2[/math][br]Write the degree, all zeros, and complete the sentence about the end behavior.[/size][br][br]Degree:                     Zeros: [br]End behavior: As x gets larger and larger in the negative direction,
Sketch a possible graph.
Check your sketch.
[i]Pause here for your teacher to check your work.[br][/i][br]Create your own polynomial for your partner to figure out.[list][*]Create a polynomial with degree greater than 2 and less than 8 and write the equation in the space given.[/*][*]Trade papers with a partner, then fill out the information about their polynomial and complete a sketch.[/*][*]Trade papers back. Check your partner’s sketch using graphing technology.[/*][/list]
Fill out this information about your partner's polynomial:[br][list][*]Degree: [/*][*]Zeros: [/*][*]End behavior: As [math]x[/math] gets larger and larger in the negative direction, [/*][/list]
Sketch your partner's polynomial.
Check your partner's sketch.
Sketch a graph for a polynomial function [math]y=f(x)[/math] that has 3 different zeros and [math]f(x)\ge0[/math] for all values of [math]x[/math].
What is a possible equation for the polynomial?
Use graphing technology to see if your equation matches your sketch.
What is a possible equation for the polynomial?
What is a possible equation of a polynomial function that has degree 5 but whose graph has exactly three horizontal intercepts and crosses the [math]x[/math]-axis at all three intercepts? Explain why it is not possible to have a polynomial function that has degree 4 with this property.
Close

Information: IM Alg2.2.10 Lesson: Multiplicity