Question

The function p(x) = –8x2 – 64x can be written in vertex form p(x) = a(x – h)2 + k, where a =

Answer 1

Means compplete the square on one side

basically get into form $f(x)=a(x-h)^2+k$


ok, group x terms
$p(x)=(-8x^2-64x)$
factor out linear coefient (-8)
$p(x)=-8(x^2+8x)$
take 1/2 of the linear coefient and square it
8/2=4, 4^2=16
add positive and negaitve of that inside parntheaese
$p(x)=-8(x^2+8x+16-16)$
factor perfect square
$p(x)=-8((x+4)^2-16)$
expand
$p(x)=-8(x+4)^2+128$

in vertex form it is $p(x)=-8(x+4)^2+128$