Question

identify the vertex and the axis of symmetry for the function.\\( g(x)=(x + 9)^2 \\)\\( \\)\\( \\)the vertex of the function 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 \((h, k)\) is the vertex of the parabola.

Step2: Rewrite the given function in vertex form

The given function is \( g(x) = (x + 9)^2 \). We can rewrite this as \( g(x) = 1(x - (-9))^2 + 0 \).

Step3: Identify \( h \) and \( k \)

Comparing with the vertex form \( g(x) = a(x - h)^2 + k \), we have \( h = -9 \) and \( k = 0 \).

Answer:

\((-9, 0)\)