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?

Answer 1

< 5, - 23 >

Explanation:

The vertex of f(x) = x² is at the origin (0, 0)

Find the vertex of g(x) = x² - 10x + 2

Given a quadratic in standard form : ax² + bx + c : a ≠ 0

The the x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

g(x) = x² - 10x + 2 ← is in standard form

with a = 1 and b = - 10, thus

`x_(vertex)` = -
`(-10)/(2)` = 5

Substitute x = 5 into g(x) for the corresponding y- coordinate

g(5) = 5² - 10(5) + 2 = 25 - 50 + 2 = - 23

vertex = (5, - 23)

Thus the translation from (0, 0 ) → (5, - 23) is

< 5, - 23 >