what value represents the vertical translation from the graph of the parent function f(x)=x² to the graph of…

Explanation:

Step1: Recall function - translation rule

For a quadratic function in vertex - form $y=a(x - h)^2+k$, the value of $k$ represents the vertical translation. The parent function is $f(x)=x^2$, and the transformed function is $g(x)=(x + 5)^2+3$.

Step2: Identify the vertical - translation value

In the function $g(x)=(x + 5)^2+3$, comparing it with the vertex - form $y=a(x - h)^2+k$, we have $k = 3$. A positive $k$ value means the graph of the parent function is shifted $k$ units up.

Answer:

C. 3