Question

identify the vertex and the axis of symmetry for the function.\\( f(x)=x^{2}+9 \\)\
the vertex of the function is \\( \square \\).\\( \text{(type an ordered pair.)} \\)

Explanation:

Step1: Recall the vertex form of a quadratic function

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

Step2: Rewrite the given function in vertex form

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

Step3: Identify the vertex

Comparing \( f(x)=1(x - 0)^2 + 9 \) with the vertex form \( f(x)=a(x - h)^2 + k \), we have \( h = 0 \) and \( k=9 \). So the vertex is \((0,9)\).

Answer:

\((0, 9)\)