Question

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2? right 5, down 23 left 5, down 23 right 5, up 27 left 5, up 27

Answer 1

Hey there! :)

Answer:

Right 5, down 23

Step-by-step explanation:

Beginning with the parent function f(x) = x²:

Find the translations of the graph g(x) by completing the square to rewrite the equation in vertex form:

g(x) = x² - 10x + 2

-2 = x² - 10x

-2 + 25 = (x² - 10x + 25)

23 = (x - 5)²

Rewrite:

g(x) = (x - 5)² - 23

The translations that we can see from this equation in vertex form are a horizontal translation of 5 units right and 23 units down. Therefore:

Right 5, down 23 is the correct choice.