Question

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function a(x) = x2 - 10x +2?

Answer 1

5 units to right and 23 units down

Explanation:

The vertex of
`f(x)=x^(2)` is at
`(0,0)`.

In order to find the vertex of function a(x), we convert the function a(x) to vertex form.

The general vertex form is
`y=a(x-h)^(2) +k`.

Here,
`(h,k)` is the vertex.

`a(x)=x^(2) -10x+2\\ a(x)=(x-5)^(2)-25+2=(x-5)^(2)-23`

So, the vertex of the graph of a(x) is at
`(5,-23)` and the vertex of f(x) is at
`(0,0)`.

Therefore, in order to translate
`(0,0)` to
`(5,-23)`, we have to move the vertex of f(x) 5 units to right and then 23 units down.