IM Alg2.2.7 Lesson: Using Factors and Zeros

M and K are both polynomial functions of x where
[math]M(x)=(x+3)(2x-5)[/math] and [math]K(x)=3(x+3)(2x-5)[/math].[br]How are the two functions alike? 
How are they different?
If a graphing window of [math]-5\le x\le5[/math] and [math]-20\le y\le20[/math] shows all intercepts of a graph of [math]y=M(x)[/math], what graphing window would show all intercepts of [math]y=K(x)[/math]?[br]
Mai graphs the function given by
[math]p(x)=(x+1)(x-2)(x+15)[/math][size=150] and sees this graph.[/size][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVYAAAFlCAYAAACwQcCAAAAgAElEQVR4Ae2dW6glR9mGRSEXYXQ2aG6EkKBCwAudUTJKjHFQY3SMcVQkEA+ZMSAhXmQMIVEMcUAE44EMUVBiNCMBEcYxA4qXugMRLxJQwStBNMLcCPEIQUOwf541/7dSu6e7V3ev6jq+Bb3X6lPV971fr2dXV1dVv6RRkgJSQApIAa8KvMRrbspMCkgBKSAFGoFVF4EUkAJSwLMCAqtnQZWdFJACUkBg1TUgBaSAFPCsgMDqWVBlJwWkgBQQWHUNbK3AM8880zzwwANb5zMngz/96U9zTotyDhqhlVL5Cgis5cc4iIcveYnfSwlgPvroo3tsZ/03v/nNehvfH3zwwfV66l/Q6O9//3vqZso+Dwr4/TV4MEhZ5KmAb7CigpsnoL3iiiv2iHPnnXc2V1111Z5tKa+4/qRsp2zbXgGBdXsNlcP/Q9D3bfn+/fvXNbwPfvCDF9VgL7vsshV8fZe7VEAF1qWUTS9fgTW9mGRpEbXJX/7yl15tf8c73rHKk3zf+MY37smbZoBLLrmk2bdvXxbNAcBfYN0TwqJXBNaiwxvOOYOgzxK51QeqXXmz72Uve9kKVjk0B+CHwOrz6kg7L4E17fhkY10X/LY1/otf/GJDEwB5t5M1AxhcU28O6Kp1t33SejkKCKzlxDKqJ8APEPpMVsvj0000A1D7O378eHP48OHm0ksvTb45AB+6/kG4ful7OQoIrOXEMqon3Jr7Bivdq2699daL/KIs9n33u99d1WgBberQElgvCmPRGwTWosMbzjmg6hOs9PfkgVjXLb7VYA2seAlcU+4jSn/b1OEf7mopvySBtfwYB/EQqHbVLucUTg8AoNoeINDOywVre19q6+gjsKYWleXsEViX07aqnGPUyHIDq88afVUXV4bOCqwZBi1Fk2O0IQqsKV4JsgkFBFZdB14UEFiHZaS2qhrrsEYl7RVYS4pmRF8Aa+gO8DnVWGlfFVgjXqCBixZYAwteanE8kRdY+6MLWDc9jOs/W3tyU0BgzS1iCdsrsPYHB7BaN7H+o7SnFAUE1lIimYAfgHVMX9LHH3+8OXnyZHP69On18ZzHNlvGQCi3poAxPiUQRpngQQGB1YOIyuKCAkzztwke7KetkU+6aDEXAIl1a4e0/Zt0zQmsBw4c2KjNJn+1Px8FBNZ8YpW8pXNud4ExyYA7xcmcwEptHh+V6lBAYK0jzkG8HAtWhqnu7u42R48eXT/QoXmACVVoCjh16lSvvX/5y18aW7761a8273nPe9brbH/++ed7z425Y2wzSUwbVbY/BQRWf1pWnxNgHfMOKqudMgTWjqeNle0sbhNBW9Sf/OQnjS133HFHc+jQofU621MGa9sXrZergMBabmyDezZnhivmBeiaaKX9fqsuZ3JrCujyQdvKVEBgLTOuUbziodOUTvDUUq+88sqLbAW0JYEVf0J3RbtIVG0IqoDAGlTusgsDqtRahxKd5GkyoD2VT9pWSe52egowDeCmlEuNleYNe0i3ySftL0MBgbWMOCbhBW2jwDJUygmsIXUJpb/K6VdAYO3XRnsmKkDNLCRABNaJAdLhwRQQWINJXX5BAmt3jEPr0m2FtoZUQGANqXbhZQGQnZ2dYF7mUmOl7TlkTT5YAFRQrwICa6802jFVAZ7yh3z6nRNYfb22ZmpMdHwcBQTWOLoXW6rAenFop3ZDuzgHbclNAYE1t4glbi9g7erwv4TZOdVYp/TvXUIr5RlWAYE1rN7FlzZmhitfIuQCVpoBBFZfUc8jH4E1jzhlYyUPaXiIFSLlAlY0EVhDXBHplCGwphOLIiwRWC8OY0hNLi5dW2IoILDGUL3gMkPWznKqsYaqxRd8aWXlmsCaVbjSN3bODFdzvRJY5yqn85ZWQGBdWuHK8g/ZtSgXsNJTQjXWun4IAmtd8V7cW8A61BmerlgnTpxYzW7FGwTcWazsLQLHjh1bv2RwyOCcwBqqC9qQXtoXTgGBNZzWVZRk0//1OQtIDaZ8MtE1iRqd+2LBIThb3jmB1WzWZx0KCKx1xDmYlwCSB1hjEkNgbUJrarru7bIBdygfgXVIHe2LqYDAGlP9AsseA1aO4aWBANhqr+0uSX1wfuKJJxpb7rnnnubaa69dr7M9tXde6e0BBV7kI1wSWEeIpEPGKwA0N80XAGw4jmYDq5mOBas1JfB5//33r9pq3W2pgXWMHuPV1ZG5KCCw5hKpjOzcBFbXFYAKaGkKsNe0sN+A6x7b/p5DUwBg7at9t/3RejkKCKzlxDIZT4bASu3SnpADHQMo23l4Rbsrr3gp5eGVwJrMZRnUEIE1qNx1FAZYAWVXAjRAk1octVSDLMdSY2UfYB2TVGMdo5KOiaGAwBpD9cLL5Ek/AF065QBW/nmoKWDpKyG9/AXW9GKSvUWARGC9EEbAOqZZI/ugy4E9Cgise+TQig8FAKv7IMpHnl155FJjBa5KdSkgsNYV7yDe8hAqBEwE1iDhVCEzFBBYZ4imU4YVAKoC6wWNaAYIocVwRLQ3tAICa2jFKyhPYH0xyDSLjO3l8OJZ+pa7AgJr7hFM0H7AGuJJeA5NAaEe5CV4GVRtksBadfiXcZ4HVwLrBW0F1mWusdRzFVhTj1CG9oUabZRDjfXAgQNBup5leJkUbbLAWnR44zgHWK+88srFC88BrIxCC9Gnd3GxVcAkBQTWSXLp4DEKMEx1aL6AMXmMOSYXsDL/gVJdCgisdcU7mLcC6wWpQ+gQLKgqaLQCAutoqXTgFAUAytI1tVxqrFN007FlKCCwlhHH5LzYv39/Z9sizQQ8KWdhykAmuyYxGxaTt9g+2z7kWOpgxSfVWIciWO4+gbXc2Eb1rK+bEbVYq8nyafOx8oBn6gil1MGKT/ZOr6jBUOHBFRBYg0teR4F9YHW9B6wcRzKw9s3j6p5n33MAq/lnNuuzDgUE1jriHNxLgLKpBso4epsFC6DauHq3iaBt+NmzZ5vTp0+vlk996lPNwYMH1+tsT+mdV/yzEFjbEaxjXWCtI87BvbzzzjsHwcr+vnZUarJ9t9D/+Mc/Glseeuih5siRI+t1tqcEVvwTWINfekkUKLAmEYbyjBiaiAXg9EHVlOgDq+3nM/WmADRgCkWl+hQQWOuLeRCP+6DCrT/DPE+ePLle6CnA9lOnTjXnzp1rjh49OmpGqBzAuqk5JEgwVEhwBQTW4JLXUWDfbTAQpe3RXbj1Z2Eb5419gCWw1nEt5eilwJpj1DKwOcSDm9TBuqmdOYMwysSZCgisM4XTacMKANalJ2JJHaxjekYMq6i9uSogsOYaucTtDjHqKAew8g9GqT4FBNb6Yh7M46WHcwqswUKpgiYqILBOFEyHj1dg6YlYBNbxsdCRYRUQWMPqXVVpgHXJW+HUwbq0/1VdTJk5K7BmFrCczOXhTe1gpRuZUn0KCKz1xTyYxwKrfl7BLrbEClLkEwtISeYs3d0oh6aAkuIpX8YrILCO10pHTlRg6Q7yKYOVJpCle0VMDIcOD6iAwBpQ7NqKGpqIxYcWqYPVJvH24avyyEsBgTWveGVlbd9ELL6cSB2sNIUo1amAwFpn3IN4zYxVXXBhIpbd3d2LJlthO7NblTAJC00BXb4HEV6FRFdAYI0egnIN6IIL0GSOUqBLGywLCajamwNs/yZlUq6xUlsXWDdFsNz9Amu5sY3uGWDdNBGLtUM++OCDeya/zn2ia8DKq2aU6lRAYK0z7kG8phY69GSc/TbDPp+A2FJfbe/ZZ59tbGFi7Pe9733rdban8mqWpR/cmU76TFMBgTXNuBRjVR9YGZEEPIErie9u22ofWHmZ4GOPPbZabrvttuZNb3rTep3tAmsxl07WjgisWYcvfeMBa3tYp0HVBSltrW6N1ZoIhjxMuY2VGji1VqU6FRBY64x7MK/379+/B5hdUMUYXsliILJjNhmZMlipcW96YeIm/7Q/XwUE1nxjl4XlAMatiQJPHmgdPnx4vVjNlYc9bKe2atuGnEwdrK7fQ35oX3kKCKzlxTQpjwArXauWSALrEqoqTx8KCKw+VFQevQoAVrvF7z1o5o6Uwbqzs7Onpj7TRZ2WqQICa6aBy8VsoFojWHloZz0ecomV7PSngMDqT0vl1KFAzWDtkEObKlFAYK0k0LHcBKw0ByyRUm4K6Ou/u4QOyjM9BQTW9GJSlEU8Ga8NrPRoEFiLuownOyOwTpZMJ0xRoEaw4vOYuQ6m6Khj81JAYM0rXtlZC2R4Qr5ESrUpYMl/JkvoqDz9KyCw+tdUOToKMIpqqdtigdURWl+TUkBgTSocZRpTG1iZAnGpduUyr5DyvBJYy4tpch4B1jFDVKcanmqNlZ4Qmot1ajTLOl5gLSueSXrD2H/aHX2nlMG61KAI3xoqv2UUEFiX0VW5OgpwWyywOoLoa/EKCKzFhzi+g4CVdkc3MTGLC1uGf548eXK9uPvc89zvqdZYNRerG6U6vwusdcY9qNdMYu3eGrPehg8gpV2ST5Yx4+xTBSv/SDQXa9BLLLnCBNbkQlKeQUDVBavBs73NXR+jQspgxUelehUQWOuNfTDPAWb7KTngcUHKuk2AfezYsd4a69NPP93Yct999626Ndk6nym882qpNuVgAVNBWysgsG4toTLYpAC3xcDGTW2wtvf1vfPqySefbGy59957m2uvvXa9zvYUwEr3MtVY3YjW911grS/mwT0GMlPAioFjxtqn2hQAWBlxplSvAgJrvbEP5rnd5rsFtmus7sOqLhC759r3lMFqNuqzTgUE1jrjHtRroNke1spILPfJucGUmi3tsWNqfCmCdcm5EYIGTYVtpYDAupV8OnmsAm2wjj1v6LgUwco/iCV8HdJB+9JTQGBNLyZFWgRs3Nt9H06mCtZ2e7IPX5VHXgoIrHnFK1treRhFbc5nElh9qqm8fCogsPpUU3n1KkAtrgawMlRXNdbey6CaHQJrNaGO6yiwcR9W+bAmxRorgx4EVh/RzTsPgTXv+GVjPU/63ZFWPgxPFay+/fShlfIIq4DAGlbvaksDNr6BI7BWezkl77jAmnyIyjAQqLbnC9jWsxTBukTNfFuddH54BQTW8JpXWWLXfAHbCpEiWGlfbc89u62fOj8/BQTW/GKWpcU2ssqn8amC1XfvB5+aKa8wCgisYXSuvhRgw7SAPpPA6lNN5eVTAYHVp5rKq1eBrvkCeg8euSNFsDLCTDXWkQEs+DCBteDgpuaa7zH0qYJ1zAQyqcVG9vhVQGD1q6dyG1AAsDKrFeDhLQHt7le8C4uHP7wPi+M2pVTBuslu7S9fAYG1/Bgn46HNF2BPzl2w0mvA1oEqcN2UUgOrpgzcFLF69gus9cQ6uqcA1dof+TSQYhi1VdvHet+rWVwnUgMr9vtu7nD91fd8FBBY84lV9pZaTRVH2mB1oct+1rvS2bNnmzNnzqyW22+/vbn66qvX62yP+c4rfOqzu8sXbStXAYG13Ngm5xm1UqultsHKrT/bLPUB6vz5840tX//615sbbrhhvc52gdUU1GdMBQTWmOpXVjZQ7QMro5WYcs9Sjk0BS4wuMz30mZcCAmte8craWqBqD6XaNVb6uVJL3d3d7ewx0OV4am2srn9d9mpbPQoIrPXEOrqn7iTQgNS99cc4trVrrkNGpwhWq5EP2a195SsgsJYf42Q8BKR9badzjBRY56imc0IoILCGUFllrBQArDs7O97USA2s/NNQjdVbeLPOSGDNOnx5Ge+7A32KYHUfwOUVHVnrUwGB1aeaymujAj470KcI1na78UZBdECRCgisRYY1XacAqy/4pAbWAwcOePMt3QjKsjEKCKxjVNIx3hSgHbJUsNokM97EUkbZKiCwZhu6PA0HrL7aIVOrsfps5sgzurLaFBBYTQl9BlGAAQK+npwLrEFCpkJmKCCwzhBNp8xXAKiWCFamOlSNdf51UdqZAmtpEU3cH6DKZCw+Uko1VtqNmW9WSQqggMCq6yCoAgxZ9TX6KjWw+vIraEBU2CIKCKyLyKpM+xSgZucLQCmB1Z0Hoc93ba9HAYG1nlgn4Slg7XsNNvuY3YqFCVk2pZTAShOHzdy1yW7tL18BgbX8GCflIcDseshjNVl7uMX6ppQaWH09lNvkt/anr4DAmn6MirOwD6xTwSSwFndpFOOQwFpMKPNxBLC2X29NDZVXYtMM0N7nevaf//ynseXb3/5284EPfGC9zvZYr2ah3XjqPwbXL30vSwGBtax4ZuENr11p3+oDU8DE601oq+zrksXLBL/zne+slk984hOrt7naOp8xweprRFkWQZSRgwoIrIPyaOcSClC7a4O1Xc6YPqEpNQWM8anto9bLVUBgLTe2yXq26baZeVtze5kgPR02/bNINiAyzLsCAqt3SZXhJgW45W+3R9IEQBvryZMnV1Adc1udUo21q914kw7aX64CAmu5sU3WM6Da1YZKV6yhB1dth1IDa9s+rdergMBab+yjee5rWKvAGi2EKniDAgLrBoG0278CtEXSzrptSgWs+NPVN3db/3R+vgoIrPnGLlvLAVHfsNYpTqUEVh//KKb4rmPTVkBgTTs+RVrXN6x1qrMC61TFdHwoBQTWUEqrnD0K+Lh1TgWsvtqM9wiklawVEFizDl++xvvonpQKWOnlcOutt+YbDFnuXQGB1bukynCMAl3DWsec5x6TEljb/XJdO/W9PgUE1vpinoTHPoaApgJWaqsCaxKXVTJGCKzJhKIuQzYNax2jRipgxRfaWZWkgCkgsJoS+gyqADW8bWt5KYFV8wQEvXySL0xgTT5EZRoIVLuGtU7xNhWwHjhwQBOwTAlcBccKrBUEOUUXfXRRSgWs9HBQjTXFqyyeTaPBeubMmea5556LZ2nTNNjw17/+NaoNP/3pT5s//vGPUW3gR/y73/0uqg1PP/108+STT862AR+2Ha2UAljPnz8ffTjrv/71r9VvY3YwPJz4v//9L7oNuAEj/v3vf3vwaLssRoP14Ycfjg7WH/7whwJr06xqRyWAdWdnZ6urV2C9IB9g/f73v7+VltueDFgfeuihbbPZ+vzvfe97i4KVUYM0YZ07d27QVoF1UJ6Ld6rGekGTbWusTGa97eirFMD64x//eGs/Lr7Kpm0RWF/Ua2mwUhJTW7785S9vLr300uaWW27phOxosH7sYx9b/UfiBW6xlttuu6352te+Fq18/L7jjjuaL33pS1Ft+OxnP9vcd999UW34/Oc/39x9991b2QBYt7mWPv7xj68mxd4mj23P/fSnP9288pWv3MqPbW04depU88lPfjKqDfhw8803R7eB96Chx7aabjr/C1/4QnPJJZes/qkC2DZkR4MVMh89erT5yEc+Em05dOhQc+ONN0YrH9+vueaa5r3vfW9UG6677rrm3e9+d1Qb3vnOdzaHDx/eygbAii9zr6k3v/nNzatf/erZ588t1z3vLW95S/OKV7wiqg033XRTgxauXaG/f/jDH179kwtdbrs8dOBllO3tvtfRnFrrS1/60hVggexll122aiagRjsarGpjvXC7oaaACzps2xRALtuOvkqhKYBXybz+9a+/IEqkv2oKeFH4EE0BNGMRcyoGLkxftKIRWF0xxnwXWC+o5AusvOtqbkoBrHfddVdz5MiRuS54OU9gfVHGpcEKVO317EOvEVKN9cWYjPomsF6QyQdYtx1jnwpYP/rRj466dpY6SGB9UdkQYH2xtP5vo8H6wgsvNCwxk2y4oH4pOmw7rDUFsPLQ6P7774/5s1j9LmP/NuluFdsGghD6t0F/bHdoNl2xuAsbDdaoV44KL1IBLkhuq+amFMBKO/E2zRlzfdd56ShwxRVXNDQRcB3Y9SywphOf6izZdvRVKmDFD6V6FaCCcOzYsVWvCABLEljrvR6iew6QmMBkbkoBrLwUUWCdG8EyziP+9BBgVJalUWDtevrFtt3dXcsn2KeVa/8ZghXcKggR8T+2HegRywbTwL2gWjINrmI7F+TclAJYsf9HP/pRtBi42sUGvF0PuV6PrpZjv+MrzUE0AbhNQoNXNSdRxd2/f/+ecmigJSOqwLxiI1SyNjk+cWbuD3pbe/EdDbAjlg34AJiITYwfFBeRPdXnGnj88cdnyZozWLkOsN+ux1hAQXhmC2v/TmcFZOZJXAsxfxP8BrgO0aENuZkujTrN2tjhAG2tlgbByo8HgznZkhHa1hEz1A/btQPbuKBDJ8pNYbZ4i0NI/fu0bl8jfcd1bQdM/IOYk2LXWImB/WOIGQd+1MDE/X3M0XPuObF+i669sMA4hB4htGj7zTVg1/IgWM1w10iM57+TpXbmtn2JT4BGDRrjsSlGbZFyKZ/xyJtmuFlCA8vTguheULYv9Ce1VeyZk7Z5qWBssPJbsFpirOsRzSnb/tHOicG259hv4vTp09F+E8YEPmHE3DuobbWw8/eA9b///W9jix3AJ8JZ4mJya4rtdTvOx6fZwicJ0fghspw4ccJHERvzcG3gO2Vb7YRPV4uNmc08oG0DF42VGwqsbRvMFX7QaMLnnMS1NfdHkAJYsZ/Kxdx/LHM0c88h/qaf+zt1j1n6O+XabwJ7YmjB9cfcFdjCMvd69KXVHrD+4Ac/WNVG3RopBbkBA6TcdlhassbKQwFsMXvcHzC11xAB/MUvfrG2gUm2XS3a2pgmvj9///vfr2349a9/3fAkmgdnLPx3pva89IWE7xYLNCFRJnrwD29u4lqyfxJT84gNVoB21VVXra/PqfZvezx3bMDErgV6WPA9dGr/Jty2xlC2cG3CJpJVwEKV3VXOHrB2HcC2tnAAzpLrkG1b6tMtF/FcwC9VZjtf/LUmiFBtOa4NlAmIbCE2rk3usUt+9wFV7DM/5tgaG6xcf5dffvkc072c074WANrcf1LbGOQywK6LbfKbcy6/A7dy4bJiTn7bnjMLrNRScYTaEqKGSlw0XMzMKIRw29SU5trMxWw2oEEMG1zb0cT+U7vbl/6OBtScqTHZMqdMi+mcc2OClbjz4MrVIMQd1JBOXI8xklUw+F1igzVNhLSFMikbG7geYVTMNAqsfQYiaIwUG2b4nIINMbT3Xab9IObkGxOs2AtIY9QQ52gV4pwUfhMp2IDWW4E1RLBURtkKUNu2mr/VfMfWOGKDFbtT6HpX9hWSp3cCa55xK8ZqahjcUgPYqbW/FMAaoxmmmOAX7IjAWnBwc3EtV7DyFF5gzeUqC2unwBpWb5XWoQBgpfbJrTULD8b62sp+/vOfN7bQxvnWt751vc72559/vqOEZTZhd5+dy5SoXHNRQGDNJVKF2fm3v/2tuffee1fLa17zmj01P7rN9PWF/MMf/tDY8uUvf7l517vetV5ne2iwFhYWueNJAYHVk5DKZpoCgPXPf/7zauFNp+0uOn1gdUuJ2cZKjxhqrEpSoEsBXRldqmhbUAW49ac/NKOGuLVmJNmYPqExwUrbqs0TEFQsFZaFAgJrFmEq20h6A1ifUL6P7dwdG6y0BytJgS4FBNYuVbQtqALAlFrr1BQTrDb6cKrNOr4OBQTWOuKctJfcVs+p/cUEK/8MQg7nTjqAMu4iBQTWiyTRhtAKANY5776KDVbgqiQFuhQQWLtU0bagCsx9wh4TrDRdCKxBL5OsChNYswpXucbO6boUE6w0XbS7iJUbHXk2VQGBdapiOn4RBea8FDE2WDWcdZFLoYhMBdYiwpi/E9QAp4IqJlh3dnYm25t/lOTBWAUE1rFK6bhFFQCsU6fgiwlWmi7cGesXFUeZZ6eAwJpdyMo02AYITPEuNlin2Kpj61JAYK0r3sl6yxP2McNYXQdigZUmizkP21zb9b1sBQTWsuObjXdzRjLFBOucAQ3ZBEOGbq2AwLq1hMrAhwLUAqfCKhZYt3lPlw+tlEf6Cgis6ceoCgvtFS1TJo6OBVaaLebMbVBFIOXkSgGBVRdCcAXsdcnuyCWesNNuSTvr2FebxwSra3twAVVg8goIrMmHqDwDqe1xO+3CiTZWwEqNFcgC100pFliZfMW1fZOd2l+fAgJrfTFPwmPaVF04AStgaoMExrS3xgIrtmk4axKXUbJGCKzJhqZsw9pgBVaA1Sa57gPr2bNnm29961ur5ZZbbmne8IY3rNfZHuKdV9hm/wDKjpK8m6uAwDpXOZ03WoH3v//9zQ033NA88sgj63PaYKXGyjFWi+0D6wsvvNDY8vDDDzc33XTTet22rwtZ6AtNFgLrQuIWkq3AWkggc3OjDVaGs9L2ysOrobe0un7GagrQ4AA3CvrepYDA2qWKti2uQBuswPS1r31tc+WVVzZHjx4d1YYZA6zWe2FxgVRA1goIrFmHL1/jARTdrtwEbGlnbW93j3G/xwArNo55Nbdrp77Xp4DAWl/Mk/XYBgmMNTAWWPvaf8farePKV0BgLT/GWXk4pf0yBlhpCxZYs7qkohgrsEaRXYX2KWCDBPr2u9tjgJVeC1Nn4XJt1vc6FBBY64hzNl5O6SMaA6xA1bqEZSOqDA2ugMAaXHIVOKQAYLVBAkPHsS8GWLFv6psONvmh/eUpILCWF9OsPZpSI4wFVnoGKEmBIQUE1iF1tC+4AtxmMwprTIoBVvrZCqxjolP3MQJr3fFPzvspk0jHACsP1+iDqyQFhhQQWIfU0b7gClAbPHDgwKhyQ4NVo65GhUUHNU0jsOoySEoBRl2N7csaGqxAf//+/UnpJWPSVEBgTTMuVVs19nY7Blg1OKDqS3O08wLraKl0YCgFGIs/5gFRaLBq1FWoKyD/cgTW/GOYpQfMC+DCk/bLkydPrhaevI/pKxoarBp1leWlFsVogTWK7HUXygAAbqndEUxA1rZdddVVo7pchQbrlD62dUdY3gusugaCK0BtFJC2wWrrfNr3IeNCgxXwjx0VNmS39pWvgMBafoyT9LANVvqvHj58eNUU8KEPfah3BqlnnnmmseWBBx5orr/++vU625d858jgyEsAAA3oSURBVBVgdZsvkhRWRiWhgMCaRBjKNuK3v/1tY4t52gYrbaxsY/nMZz7TvOpVr7JD93wCYFs47tChQ+t1ti8J1p2dHYF1TzS00qeAwNqnjLZ7U4CaJcvQywTdwsZOeB26KWBs/1rXF32vUwGBtc64R/e6XWN1DRo7SCAkWMfa5Pqh7/UqILDWG/uonrfBaj0FaGflba379u3beNsdEqzYy/u4lKTAGAUE1jEq6ZjgCox5UBQSrLTfYpOSFBijgMA6RiUdE1wBaq2bulyFBCu2jJ3OMLhYKjA5BQTW5EIig1BgTF/W0GDdBHpFTgqYAgKrKaHPpBQYMy4/JFhpBhgzzDYpEWVMNAUE1mjSq+AhBXhYtKlNMzRYsUlJCoxRQGAdo5KOCa7AmL6sIcGqwQHBL4GsCxRYsw5f2cZv6pAfEqybbCk7EvJuqgIC61TFdHwwBTbNyxoKrBocECzkxRQksBYTyvIcoY2V/qN9KRRYNTigLwLa3qeAwNqnjLZHV4B+o0NdnEKBVYMDol8K2RkgsGYXsnoMBqpMLt2XQoEVOzQ4oC8K2t6lgMDapYq2JaGAzR/QZ0wosOrNAX0R0PY+BQTWPmW0PboCtG3y/qu+FAqstPXqzQF9UdD2LgUE1i5VtG0xBeylgcxidfTo0Yb+qpZoy2T7sWPHGo5jGermFBKsGhxgUdLnGAUE1jEq6RhvCrhvZ+U7k62QAJf73do0ASvdnbpSKLBig/sPoMsWbZMCrgICq6uGvgdXwOY45QGRWyu07dyGu9tdA0OC1S1X36XAJgUE1k0Kaf9iCjCpiXWnagOUdRKf7uQnTzzxRGPLPffc01x77bXrdbb7fucVUN+/f/9iGijjMhUQWMuMa1JefeMb32hY3Hdeuc0AGNsHVsBr8OU4zrPl/vvvX7XJ2jqfS4DVIJ+UqDImaQUE1qTDU4ZxTz31VGMLHgFAYMXDKUvA0x1lZU0BQ9MHhmgKwC5r+zVb9SkFNikgsG5SSPu9KgBU6UJ17ty5Znd3d7UAWLYDML4DU3t4xa34gQMHOm0IBVa3xtxpiDZKgZYCAmtLEK0uqwCgBFTuYk/9qbECVLdNdWgClBBgbbfxLquOci9FAYG1lEgW7Edfl6tQYO3rlVCw5HJtSwUE1i0F1OnLK0B7axfcQoBVfViXj2+JJQisJUa1MJ9oe3WbB8y9pcG6aeSX2aFPKdBWQGBtK6L15BSw9ti2YUuDlVoyk20rSYGpCgisUxXT8cEV6Jvlammwah7W4KEupkCBtZhQlusINceuWa6WBis1Zev2Va668mwJBQTWJVRVnl4V6GvrXBqsQBW4KkmBqQoIrFMV0/FRFGC8PoMI3LQ0WOnD6o4Gc8vWdykwpIDAOqSO9iWjQBfklgYrzQ9d3bySEUWGJKuAwJpsaGSYq0DXbfnSYKUPq5IUmKOArpw5qumc4Ap0PUhaEqw0O2i6wOBhLqZAgbWYUJbtCLfkNAe4aUmwdpXnlq3vUmBIAYF1SB3tS0aBrslYlgRrVw05GTFkSPIKCKzJh6gsAwEkNU+GqTIHgL39lFtvRjmxj8W2u963J2NZEqx65bWrvL5PVUBgnaqYjt9KAfqkspD4tAmtufXe1Ge0PRnLkmAF7upqtVWoqz5ZYK06/HGdB6wAjGRgbfdVdS1s9wxYEqw7OzvqauWKr++TFBBYJ8mlg30qACitVghQDZxuE4FbHjXaw4cPr5oJaCo4fvx4c/DgwfU623y980pdrVzl9X2qAgLrVMV0/GQFbrzxxobFfZkgbZhd7ahkTk22a1YparW8lfWf//znavnmN7/ZHDlyZL3Odh9gpZyu8ic7rhOqVUBgrTb08RwHqH1QNau6wNbuGbBUU4BmtbIo6HOuAgLrXOV03iwFgBYvBzx58uR6AZhsP3Xq1Oolg0ePHu2c2JoC3Z4BS4GVJgdq1EpSYK4CAutc5XTeLAWAKLfa7sKtPwvbqMkOPcDiYRfHkZYCa98bC2Y5rJOqVEBgrTLs+TptD7jwYCmwUqM2eOerlCyPqYDAGlN9lT1ZAd59RY2StBRYaW6gBq0kBeYqILDOVU7nRVGAmiQ1StISYKUZQpOvRAltUYUKrEWFs3xnqElaH9MlwKoeAeVfQyE8FFhDqKwyvCpAVyxqrkuAVT0CvIaq2swE1mpDn6/j9tR+CbBa3vmqI8tTUEBgTSEKsmGSAtQq6R2wBFj1OpZJodDBPQoIrD3CaHO6CtgggyXAqh4B6cY9J8sE1pyiJVtXCtgDLN9gpd22ayitZJcCUxUQWKcqpuOTUAAA3n333es+rT6McvvI+shPedSrgMBab+yz9pyHTDfffLNXsLqjurIWR8ZHV0BgjR4CGTBHAR5gXXPNNV7BqrcGzImEzulSQGDtUkXbFlWA0U3nzp1rdnd395TDBC1sH5qExU6gPfTyyy/3ClZ35iwrR59SYI4CAusc1XTObAV4os+UfHxatykyA6r25gBu89k/lOwBFhNd+0iAWkNZfSipPFBAYNV1EFUBgxkPjtzJr8c8nafG+ra3vc2L/Xpw5UVGZfL/CgisuhSiKMDtPpNd24TS1FKpNVqylwzaun0+++yzjS0c87rXvW69zva5r2bRgytTWJ8+FBBYfaioPAYVOH/+fGMLBwJQgApMrZYKJN221T6wnj17tnnsscdWy3XXXdfs27dvvc72uWDVHKyDIdTOiQoIrBMF0+HTFbjrrrsaFvdlgpYL7aq0lwJat8bK9k3pK1/5ynqmq03HDu239lo+laSADwUEVh8qKo/ZChhYqbnyMIsE4PpqrG5BjLy69NJL9wDZ3T/2Ow/KxoB8bH46TgoIrLoGgirAQ6LDhw83vDAQmFlTAEbQzsk+trvNAn0GAlYeYBmQ+47btJ3zra1307HaLwXGKCCwjlFJxySpAGA9ePDgqNrtkAPUjjd17xo6X/ukQFsBgbWtiNazUQCwXn/99Vu3s2pGq2xCno2hAms2oZKhbQUAKz0LaDqYW+NU+2pbVa37UEBg9aGi8oiigIGV9tG5baTbnBvFaRWahQICaxZhkpFdChhY6abFzP9zEv1X59Z255Snc+pQQGCtI85FemlgxTmGxo7pSeAKwfwE9sZXd7u+S4FtFRBYt1VQ50dTwAUrXbWmNgdofoBooSu+YIG1+BCX66ALVm7npzYH0Azg9qMtVyl5FloBgTW04irPmwIuWMl0SnOANQNoGKu3cCgjRwGB1RFDX/NSoA1WmgNYxiQ1A4xRScfMVUBgnauczouuQBus1EJ3dnZWcw1sMo5mA/UG2KSS9s9VQGCdq5zOi65AG6wYxPBUaqNDie5ZYybSHspD+6TAkAIC65A62pe0Al1gHdOnlYleNsE3acdlXPIKCKzJh6gsA3lYdOrUqdUsVidOnFi96woPuY3njQK2uHOz9inQBVaOpdbaN+OV1Vb10KpPVW33oYDA6kNF5TFaATrxW9smkLN5V/nOgyc+WQDtptQHVsqgrbU9YACYqm11k6ra70MBgdWHispjlgKAzto6gWlfLbMv8z6wcjy3+kDU4EpZ9Fsd22ugr0xtlwJjFBBYx6ikY7wqAES55Qdybu0VENL+eezYsd4a61NPPdXYct99961qvLbOp/vOK+DKkFXypAYrqHoNozIbUEBgHRBHu/woYC//45PEbb7VULtgx76+V6X86le/amz53Oc+17z97W9fr7PdBauVBbyt5urHI+UiBYYVEFiH9dFeDwr87Gc/a2xpZ0cba9eDJGsiaB/vrg81BbjH6bsUCK2AwBpa8crLcx9K8d0A6m6nxmoPtYbkEliH1NG+mAoIrDHVr7BsgybgZPZ/u0V3t9M80FWLbcslsLYV0XoqCgisqURCdkxWQGCdLJlOCKSAwBpIaBXjXwGB1b+mytGPAgKrHx2VSwQFBNYIoqvIUQoIrKNk0kEpKiCwphgV2YQCAquug2wVEFizDV3xhgusxYe4XAcF1nJjm7tnAmvuEazYfoG14uAn7rrAmniAZF6/AgJrvzbaE1cBgTWu/ip9CwUE1i3E06mLKiCwLiqvMl9SAYF1SXWV9zYKCKzbqKdzoyogsEaVX4UPKCCwDoijXWkrILCmHZ+arRNYa45+5r4LrJkHsGDzBdaCg5u6a8xu5b6O5c4771xNF+jOejXkg8A6pI72xVRAYI2pfsVl89oUpgc0sD766KPr70wlCFw3JYF1k0LaH0sBgTWW8hWXy6TWQJU5WA2s1FZZt9T3ahbbz6fA6qqh7ykpILCmFI1KbLHXsbhgZZsL1r43CJw9e7Y5c+bMarn99tubq6++er3O9vY7ryqRVG4mpoDAmlhASjTn+PHjDcsjjzyyqqG6b2a1Giu3/mPAev78+WZoEVhLvILy80lgzS9m2Vn83HPPNbbYAypqpNzu884r2ldpczXg4uCYpoDshJDB1SggsFYT6vQcdZsCaHcFtru7u82xY8fWba/pWS2LpMBmBQTWzRrpiIUUAKbu7T/r7ZrrQkUrWymwqAIC66LyKnMpIAVqVEBgrTHq8lkKSIFFFRBYF5VXmUsBKVCjAgJrjVGXz1JACiyqgMC6qLzKXApIgRoVEFhrjLp8lgJSYFEFBNZF5VXmUkAK1KiAwFpj1OWzFJACiyogsC4qrzKXAlKgRgUE1hqjLp+lgBRYVAGBdVF5lbkUkAI1KiCw1hh1+SwFpMCiCgisi8qrzKWAFKhRAYG1xqjLZykgBRZVQGBdVF5lLgWkQI0K/B8N/IaW/J6L7QAAAABJRU5ErkJggg==[/img][br]She says, “This graph looks like a parabola, so it must be a quadratic.”[br]Is Mai correct? Use graphing technology to check.[br]
Explain how you could select a viewing window before graphing an expression like [math]p(x)[/math] that would show the main features of a graph.
Using your explanation, what viewing window would you choose for graphing [math]f(x)=(x+1)(x-1)(x-2)(x-28)[/math]?[br]
Select some different windows for graphing the function [math]q(x)=23(x-53)(x-18)(x+111)[/math]. [br]What is challenging about graphing this function?
Check your equation using graphing technology.
Write a possible equation for a polynomial whose graph has the following horizontal intercepts.
[math](4,0)[/math]
[math](0,0)[/math] and [math](0,4)[/math]
[math](\text{-}2,0)[/math], [math](0,0)[/math] and [math](4,0)[/math]
[math](\text{-}4,0)[/math], [math](0,0)[/math] and [math](2,0)[/math]
[math](\text{-}5,0)[/math], [math](\frac{1}{2},0)[/math] and [math](3,0)[/math]
Bezárás

Információ: IM Alg2.2.7 Lesson: Using Factors and Zeros