Question

the graph shows the axis of symmetry for a quadratic function f(x). which could be the function? \\( f(x) = (x + 4)^2 \\) \\( f(x) = x^2 + 4 \\) \\( f(x) = (x - 4)^2 \\) \\( f(x) = x^2 - 4 \\)

Explanation:

Step1: Recall axis of symmetry formula

For a quadratic function in vertex form \( f(x) = (x - h)^2 + k \), the axis of symmetry is \( x = h \).

Step2: Identify axis of symmetry from graph

The dashed line (axis of symmetry) is at \( x = 4 \).

Step3: Analyze each function's axis of symmetry

• \( f(x) = (x + 4)^2 \): Axis is \( x = -4 \) (since \( h = -4 \)).
• \( f(x) = x^2 + 4 \): Axis is \( x = 0 \) (since \( h = 0 \)).
• \( f(x) = (x - 4)^2 \): Axis is \( x = 4 \) (since \( h = 4 \)).
• \( f(x) = x^2 - 4 \): Axis is \( x = 0 \) (since \( h = 0 \)).

Answer:

\( f(x) = (x - 4)^2 \) (Option: \( f(x) = (x - 4)^2 \))