Question

identify the vertex, axis of symmetry, and direction of the graph of each function. compare the width of the graph to the width of the graph of ( f(x)=x^2 ) ( g(x)=(x - 5)^2 - 4 ) the vertex is \\( \square \\). (type an ordered pair.)

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a quadratic function is \( g(x) = a(x - h)^2 + k \), where the vertex is \((h, k)\).

Step2: Identify \( h \) and \( k \) from \( g(x)=(x - 5)^2 - 4 \)

In the function \( g(x)=(x - 5)^2 - 4 \), we can see that \( h = 5 \) and \( k = - 4 \).

Answer:

\((5, -4)\)