Question

identify the vertex and the axis of symmetry for the function
$f(x)=x^2 - 9$

the vertex of the function is
(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. For the function \( f(x)=x^2-9 \), we can rewrite it as \( f(x) = 1(x - 0)^2-9 \).

Step2: Identify the vertex

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

Step3: Find the axis of symmetry

The axis of symmetry of a parabola in the form \( f(x)=a(x - h)^2 + k \) is the vertical line \( x = h \). Since \( h = 0 \), the axis of symmetry is \( x = 0 \) (the y - axis).

Answer:

The vertex of the function is \((0, - 9)\) and the axis of symmetry is \( x = 0 \). For the vertex (as asked in the box), the answer is \((0, - 9)\)