Question

identify the vertex and the axis of symmetry for the function.\\( f(x)=x^2 + 5 \\)\
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 \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

Step2: Rewrite the given function in vertex form

The given function is \( f(x) = x^2 + 5 \). We can rewrite it as \( f(x) = 1(x - 0)^2 + 5 \).

Step3: Identify the vertex

Comparing \( f(x) = 1(x - 0)^2 + 5 \) with the vertex form \( f(x) = a(x - h)^2 + k \), we have \( h = 0 \) and \( k = 5 \). So the vertex is \((0, 5)\).

Answer:

\((0, 5)\)