Question

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = –8x + x2 + 7 ?

left 4, down 9
left 4, up 23
right 4, down 9
right 4, up 23

Answer 1

The vertex form of the function:
g ( x ) = x² - 8 x + 7 = ( x² - 8 x + 16 ) - 16 + 7 =
= ( x - 4 )² - 9
Answer:
C ) right 4, down 9.

Answer 2

Vertex of x^2 = (0,0)

Vertex of x^2 - 8x + 7

Find the roots by factoring
(x - 7)( x -1 )=0
x= 7, x = 1
middle: [7+1]/2 = 8/2 = 4
g(4) = 4^2 -8(4) + 7 = 16 - 32 + 7 = -9
Vertex = (4,-9)

Then the translation is right 4, down 9. This is the first option.