Question

what value represents the vertical translation from the graph of the parent function $f(x)=x^2$ to the graph of the function $g(x)=(x+5)^2+3$?
-5
-3
3
5

Explanation:

Step1: Recall quadratic vertex form

The vertex form of a quadratic function is $g(x) = (x-h)^2 + k$, where $k$ is the vertical translation from the parent function $f(x)=x^2$.

Step2: Identify $k$ in given function

For $g(x)=(x+5)^2+3$, rewrite $x+5$ as $x-(-5)$ to match the vertex form: $g(x) = (x-(-5))^2 + 3$. Here, $k=3$.

Answer:

3