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

Vertex form of the function g(x) is:
g (x) = x² - 10 x + 2 = x² - 10 x + 25 - 25 + 2=
= ( x - 5 )² - 23
h = 5, k = - 23
Answer: A) Right 5, down 23.

Answer 2

`5` units to the right and
`23` units down

Explanation:

we have

`f(x)=x^(2)`

This is a vertical parabola open upward with vertex at point
`(0,0)`

`g(x)=x^(2) -10x+2`

Step 1

Convert the function g(x) into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`g(x)-2=x^(2) -10x`

Complete the square. Remember to balance the equation by adding the same constants to each side

`g(x)-2+25=x^(2) -10x+25`

`g(x)+23=x^(2) -10x+25`

Rewrite as perfect squares

`g(x)+23=(x-5)^(2)`

`g(x)=(x-5)^(2)-23`

The function g(x) is a vertical parabola with the vertex at point
`(5,-23)`

Step 2

Find the rule of the translation

`(0,0)-------> (5,-23)`

`(x,y)-------> (x+5,y-23)`

That means

The translation is
`5` units to the right and
`23` units down