Question

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

Explanation:

Step1: Recall Vertex Form Translation

The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \( k \) represents the vertical translation (up if \( k>0 \), down if \( k<0 \)) from the parent function \( f(x)=x^2 \).

Step2: Identify \( k \) in \( g(x) \)

For the function \( g(x)=(x + 5)^2 + 3 \), comparing with \( y = a(x - h)^2 + k \), we have \( k = 3 \). This \( k \) value is the vertical translation.

Answer:

3