document.write( "Question 329090: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=2x^2-8x+19 \n" ); document.write( "

Algebra.Com's Answer #235833 by Fombitz(32388) $\"\"$ $\"About$

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Complete the square to convert to vertex form, $\"y=a%28x-h%29%5E2%2Bk\"$ where the vertex is (h,k).
\n" ); document.write( " $\"f%28x%29=2x%5E2-8x%2B19\"$
\n" ); document.write( " $\"f%28x%29=2%28x%5E2-4x%2B4%29%2B19-2%284%29\"$
\n" ); document.write( " $\"f%28x%29=2%28x-2%29%5E2%2B11\"$
\n" ); document.write( "Comparing,
\n" ); document.write( "(h,k)=(2,11)
\n" ); document.write( "The vertex lies on the axis of symmetry, $\"x=2\"$ .
\n" ); document.write( "The vertex y value is the function's max or min value.
\n" ); document.write( "The sign of the $\"x%5E2\"$ coefficient determines whether it's max or min.
\n" ); document.write( "Since the coefficient of $\"x%5E2\"$ is positive, the parabola opens upward and the vertex value is a minimum.
\n" ); document.write( " $\"ymin=11\"$
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