Answer
$\left(\displaystyle \frac{5}{2}, -32\right)$
Work Step by Step
$ f(x)=a(x-h)^{2}+k^{2},\qquad$ vertex: (h,k)
(solved as in example 4)
$(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$
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$y=4x^{2}-20x-7$
$=4(x^{2}-5x)-7$
$=4(x^{2}-2\displaystyle \cdot\frac{5}{2}\cdot x+\frac{25}{4}-\frac{25}{4})-7$
$=4(x-\displaystyle \frac{5}{2})^{2}-7-4(\frac{25}{4})$
$=4(x-\displaystyle \frac{5}{2})^{2}-32$
Vertex: $\left(\displaystyle \frac{5}{2}, -32\right)$.
