Question

a quadratic function $y = f(x)$ is plotted on a graph and the vertex of the resulting parabola is $(-6, 5)$. what is the vertex of the function defined as $g(x) = f(x) - 3$?

Explanation:

Step1: Recall vertical shift rule

For a function \( y = f(x) \), the transformation \( g(x)=f(x)-k \) (where \( k>0 \)) represents a vertical shift down by \( k \) units. The \( x \)-coordinate of the vertex remains the same, and the \( y \)-coordinate changes by subtracting \( k \).

Step2: Apply the rule to the vertex

The vertex of \( f(x) \) is \( (-6, 5) \). For \( g(x)=f(x)-3 \), we are shifting the graph of \( f(x) \) down by 3 units. So the \( x \)-coordinate of the vertex of \( g(x) \) is still \( -6 \), and the \( y \)-coordinate is \( 5 - 3=2 \).

Answer:

The vertex of \( g(x) \) is \((-6, 2)\)