Question

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Answer 1

The general equation for the vertex form of parabola is,

$y=a(x-h)^2+k$

Simplify the equation to obtain the vertex form of parabola equation.

$\begin{gathered} y=x^2+16x+71 \\ y=x^2+2\cdot x\cdot8+(8)^2-(8)^2+71 \\ y=(x+8)^2-64+71 \\ y=(x+8)^2+7 \\ y=1\cdot(x+8)^2+7 \end{gathered}$

So vertex form of parabola equation is,

$y=1(x+8)^2+7$