Question

How is the graph of ​f(x)=(x-7)^2+4 generated from the graph of ​g(x)​=x^2
?

Answer 1

Answer: 7 units right and 4 units up.

Explanation:

Parabolas are written in the vertex form of y = a(x - h)² + k where a is the amplitude, -h is the horizontal shift, and k is the vertical shift. From the given equation, we see that we have a shift of 7 units right and a shift of 4 units up.

`f(x)=(x\boxed{-7})^2+4 \;\; \rightarrow \;\; \text{7 units right}`

`f(x)=(x-7)^2\boxed{+4} \;\; \rightarrow \;\; \text{4 units up}`

I have also attached a graph of both of these functions below, see attached.