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

Answer:

5 units to right and 23 units down

Step-by-step 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.