Question

identify the vertex and the axis of symmetry for the function.
$f(x)=x^{2}+9$
the vertex of the function is (0,9).
(type an ordered pair)
the axis of symmetry of the function is
(type an equation.)

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 and the axis of symmetry is \( x = h \).

Step2: Rewrite the given function in vertex form

The given function is \( f(x) = x^2 + 9 \), which can be written as \( f(x) = 1(x - 0)^2 + 9 \).

Step3: Identify the axis of symmetry

From the vertex form, we see that \( h = 0 \). So the axis of symmetry is \( x = 0 \).

Answer:

The axis of symmetry of the function is \( x = 0 \)