document.write( "Question 969084: Write the function in the form f(x)=a(x-h)^2+k by completing the square . F(x)=x^2+16x-9 \n" ); document.write( "

Algebra.Com's Answer #592072 by MathLover1(20849) $\"\"$ $\"About$

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the function $\"F%28x%29=x%5E2%2B16x-9\"$ in the form $\"f%28x%29=a%28x-h%29%5E2%2Bk\"$ will be:\r
\n" ); document.write( "\n" ); document.write( " $\"F%28x%29=%28x%5E2%2B16x%29-9\"$ ....recall the rule: $\"a%5E2%2B2ab%2Bb%5E2=%28a%2Bb%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "when you compare it to your function, you can see that $\"a=1\"$ and $\"2ab=16\"$ \r
\n" ); document.write( "\n" ); document.write( "since we need $\"b\"$ to complete the square, we can calculate it from $\"2ab=16\"$
\n" ); document.write( "=> $\"b=16%2F2a\"$ => $\"b=16%2F%282%2A1%29\"$ => $\"b=16%2F2\"$ => $\"b=8\"$ \r
\n" ); document.write( "\n" ); document.write( "so, we add and subtract $\"b%5E2=8%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"F%28x%29=%28x%5E2%2B16x%2B8%5E2%29-8%5E2-9\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"F%28x%29=%28x%2B8%29%5E2-64-9\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"F%28x%29=%28x%2B8%29%5E2-73\"$ where $\"h=-8\"$ and $\"k=-73\"$ ;so, vertex is at ( $\"-8\"$ , $\"-73\"$ )\r
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