Answer: p(x) = -8(x+4)^2 + 128
Step-by-step explanation:
[tex]\begin{array}{l}Convert\ p(x)=-8x^2-64x\ to\ \text{vertex form}\\\\p(x)=-8\left[x^2+8\right]\\\\p(x)=-8\left[x^2+2\cdot x\cdot4+4^2-4^2\right]\ \longrightarrow h=\frac{-b}{2a}=\frac{-16}{2\left(2\right)}=-4\\\\p(x)=-8\left[(x+4)^2-16\right]\\\\p(x)=-8(x+4)^2+128\\\\So\ we\ have\ got,\ a=-8,\ h=-4,\ k=128\end{array}[/tex]
