document.write( "Question 952421: What is the quadratic equation whose roots are -1,5 and passes through the point (1,1). Please show your work. \n" ); document.write( "

Algebra.Com's Answer #581657 by MathLover1(20849) $\"\"$ $\"About$

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first you are looking for the quadratic equation $\"y=ax%5E2%2Bbx%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( "since you are given roots $\"+x%5B1%5D=-1\"$ , $\"x%5B2%5D=5\"$ , you will use zero product theorem to find equation:\r
\n" ); document.write( "\n" ); document.write( " $\"%28x-x%5B1%5D%29%28x-x%5B2%5D%29=0\"$
\n" ); document.write( " $\"%28x-%28-1%29%29%28x-5%29=0\"$
\n" ); document.write( " $\"%28x%2B1%29%28x-5%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( "and passes through the point ( $\"1\"$ , $\"1\"$ ),so we need a constant $\"c\"$ to multiply zero product using given point \r
\n" ); document.write( "\n" ); document.write( " $\"y=c%28x%2B1%29%28x-5%29+\"$ ...........now if you sub in $\"x=1\"$ and $\"y=1\"$
\n" ); document.write( " $\"1=c%281%2B1%29%281-5%29+\"$
\n" ); document.write( " $\"1=c%282%29%28-4%29+\"$
\n" ); document.write( " $\"1=-8c\"$
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\n" ); document.write( "giving $\"c=-%281%2F8%29\"$ \r
\n" ); document.write( "\n" ); document.write( "and, we have\r
\n" ); document.write( "\n" ); document.write( " $\"y=-%281%2F8%29%28x%2B1%29%28x-5%29\"$
\n" ); document.write( " $\"y=-%281%2F8%29%28x%5E2-4+x-5%29\"$
\n" ); document.write( " $\"y=-%281%2F8%29x%5E2%2Bx%2F2%2B5%2F8\"$ \r
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