document.write( "Question 1128483: equation of the quadratic function whose graph passes through each set of points(-3,2),(-1,0),(1,6) how do I set this up and solve\r
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Algebra.Com's Answer #744940 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "equation of the quadratic function is:\r
\n" ); document.write( "\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( "if graph passes through each set of points ( $\"-3\"$ , $\"2\"$ ),( $\"-1\"$ , $\"0\"$ ),( $\"1\"$ , $\"6\"$ ), use them to set up system of equations and calculate $\"a\"$ , $\"b\"$ , and $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ ....use ( $\"-3\"$ , $\"2\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"2=a%28-3%29%5E2%2Bb%28-3%29%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2=9a-3b%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c=2-9a%2B3b\"$ ..........eq.1\r
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\n" ); document.write( "\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ ....use ( $\"-1\"$ , $\"0\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"0=a%28-1%29%5E2%2Bb%28-1%29%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=a-b%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c=b-a\"$ ..........eq.2\r
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\n" ); document.write( "\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ ....use ( $\"1\"$ , $\"6\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"6=a%28-1%29%5E2%2Bb%281%29%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"6=a%2Bb%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c=6-a-b\"$ .........eq.3\r
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\n" ); document.write( "\n" ); document.write( "from eq.1 and eq.2 we have:\r
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\n" ); document.write( "\n" ); document.write( " $\"2-9a%2B3b=b-a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3b-b=9a-a-2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2b=8a-2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b=4a-1\"$ ...........(a}\r
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\n" ); document.write( "\n" ); document.write( "from eq.2 and eq.3 we have: \r
\n" ); document.write( "\n" ); document.write( " $\"b-cross%28a%29=6-cross%28a%29-b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b=6-b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b%2Bb=6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2b=6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28b=3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "go to $\"b=4a-1\"$ ...........(a}, substitute $\"b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3=4a-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3%2B1=4a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"4=4a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28a=1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "go to $\"c=b-a\"$ ..........eq.2, substitute $\"b\"$ and $\"a\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"c=3-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28c=2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "your equation is: $\"y=x%5E2%2B3x%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "check points on a graph:
\n" ); document.write( "( $\"-3\"$ , $\"2\"$ ),( $\"-1\"$ , $\"0\"$ ),( $\"1\"$ , $\"6\"$ )\r
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