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

Question

1 month ago

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

n p, reflect the graph of f(x) = x2 across the x-axis, vertically stretch the graph by a factor of 8, shift the graph units, and then shift the graph units.

Mathematics

2 answers:

AnnZ [12.3K] · Answer 1 · 2026-02-24T17:21:42+03:00

AnnZ [12.3K]1 month ago

9 0

A= -8

h= -4

k= 128

Shift the graph 4 units to the left.

Then elevate the graph by 128 units.

Zina [12.3K] · Answer 2 · 2026-02-24T17:19:54+03:00

Solution:

The task is to convert the given function into vertex form.

$p(x) =-8x^2-64x$

The formula for the vertex form is

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

Hence, we need to rewrite P(x) in that format.

$p(x) =-8x^2-64x\\
\\
P(x)=-8[x^2+8]\\
\\
P(x)=-8[x^2+2.x.4+4^2-4^2]\\
\\
p(x)=-8[(x+4)^2-16]\\
\\
P(x)=-8(x+4)^2+128\\$

So we have $a=-8, h=-4, k=128$

This implies a vertical stretch of the graph by a factor of 8.

The parent function shifts upwards by 128 units.

Additionally, it shifts to the left by 4 units.