the graph shows g(x) which is a translation of f(x)=x^2. write the function rule for g(x). Show all work.

Question

https://drive.google.com/a/oxfordschools.org/file/d/18nvGKSvASduq_Ot_wwm4iQ8nMYn6RTxB/view?usp=drivesdk

This is a link to the photo of the graph.

Answer 1

The vertex form of a parabola is f(x)=a(x-h)²-k where (h,k) is the vertex.

In your case, we know the vertex is at (7,6), which allows us to fill in the h and k as follows:

(x-7)²+6

Now, the only question is the value of a. A is the stretch or compression factor, telling us whether the graph is "fatter" or "skinnier" than the parent function. In your case, since we can see that the graph goes over 1 and up 1 from the vertex, it is the same shape as the parent function, and a=1. So the vertex form is

f(x)= (x-7)²+6

If the answer is to be given in standard form, expand the (x-7)² and then combine like terms.

Best wishes