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:

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

Step3: Identify the vertex

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

Answer:

\((0, -8)\)