Question

I suck at math lmaoo
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 function 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.

Answer 1

Given  : The function p(x) = –8x² – 64x can be written in vertex form

p(x) = a(x – h)² + k,

To Find : a , h and k

Solution:

p(x) = –8x² – 64x

=> p(x) = - 8 ( x²  + 8x )  

Add and subtract (8/2)²  = 4²   = 16  in bracket

so that ( x + y)²  = x²  + y² + 2xy identity can be applied

=> p(x) = - 8 ( x²  + 8x + 16 - 16 )  

=>  p(x) = - 8 ( x²  + 8x + 16)   + 128

=>  p(x) = - 8 ( x +4 )²  + 128

=>  p(x) = - 8 ( x  - (-4) )²  + 128

comparing  with   p(x) = a(x – h)² + k,

a = - 8

h =  - 4

k = 128

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