Write a rule of g

Question

The graph of h is a translation 8 units up and 3 units right of the graph of f(x)=x²-3x. For each value of x, g(x) is 125% of h(x)

Answer 1

The graph of h is a translation 8 units up and 3 units right of the graph of f(x)=x²-3x

h(x) = f(x-3) + 8

       = (x-3)² - 3 (x-3) + 8

 

g(x) is 125% of h(x)

g(x) = 1.25 h(x)

       = 1.25 [f(x-3) + 8]

       = 1.25 [(x-3)² - 3 (x-3) + 8]

or

g(x) = 1.25 [x² - 9x + 26]

       = 1.25x² - 11.25 x + 32.5

Answer 2

First, write the f(x) in vertex form.  We will use the vertex form as our reference point for translation.

 

f(x) = (x² - 3x + 9/4) - (9/4)

 

f(x) = (x - 3/2)² - 9/4

 

 

Vertex of f(x) is (3/2 , -9/4).  Move the x-coordinate of vertex 3 units to the right and y-coordinate of vertex 8 units up.

 

h(x) = (x - 9/2)² - (23/4)

 

You can put h(x) in standard form.

 

g(x) = 1.25h(x)