document.write( "Question 1100969: Write the quadratic function in vertex form.\r
\n" ); document.write( "\n" ); document.write( "y = x^2 + 16x + 74 \n" ); document.write( "

Algebra.Com's Answer #715528 by greenestamps(13200) $\"\"$ $\"About$

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Vertex form is
\n" ); document.write( " $\"y+=+a%28x-h%29%5E2%2Bk\"$

\n" ); document.write( "The vertex is at (h,k); the parabola opens upward if a>0 or downward if a<0.

\n" ); document.write( "You need to complete the square in x in order to be able to write the equation in that form.

\n" ); document.write( "Note the leading coefficient of 1 makes this example easier; we know immediately that the coefficient a in the vertex form is 1, so we can ignore it. Then
\n" ); document.write( " $\"y+=+x%5E2%2B16x%2B74\"$
\n" ); document.write( " $\"y+=+%28x%5E2%2B16x%29+%2B+74\"$
\n" ); document.write( " $\"y+=+%28x%5E2%2B16x%2B64%29+%2B+74+-+64\"$ [complete the square; half of 16 is 8; 8 squared is 64. Then since you added 64 inside the parentheses you need to subtract 64 outside]
\n" ); document.write( " $\"y+=+%28x%2B8%29%5E2%2B10\"$

\n" ); document.write( "This is vertex form. The vertex (minimum value of the function) is at (-8,10). \n" ); document.write( "

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