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 vertex form symmetry

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

Step2: Analyze each option

• \( f(x)=(x + 4)^2=(x - (-4))^2 \): Axis of symmetry \( x=-4 \).
• \( f(x)=x^2 + 4=(x - 0)^2+4 \): Axis of symmetry \( x = 0 \).
• \( f(x)=(x - 4)^2 \): Axis of symmetry \( x = 4 \).
• \( f(x)=x^2 - 4=(x - 0)^2-4 \): Axis of symmetry \( x = 0 \).

From the graph, the axis of symmetry is \( x = 4 \), so the function is \( f(x)=(x - 4)^2 \).

Answer:

\( \boldsymbol{f(x)=(x - 4)^2} \) (corresponding to the option " \( f(x)=(x - 4)^2 \) ")