Question

identify the vertex and the axis of symmetry for the function f(x) = x² + 8 the vertex of the function is (type an ordered pair )

Explanation:

Step 1: 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.

Step 2: Rewrite the given function in vertex form

The given function is \( f(x)=x^2 + 8 \). We can rewrite it as \( f(x)=1(x - 0)^2+8 \).

Step 3: Identify the vertex

Comparing \( f(x)=1(x - 0)^2 + 8 \) with the vertex form \( f(x)=a(x - h)^2 + k \), we have \( h = 0 \) and \( k=8 \). So the vertex of the function is \((0,8)\).

Answer:

\((0, 8)\)