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 quadratic $f(x)=(x-h)^2+k$, axis is $x=h$. For $f(x)=x^2+k$, axis is $x=0$.

Step2: Identify axis from graph

Graph shows axis $x=4$.

Step3: Match to options

Find option with $h=4$: $f(x)=(x-4)^2$.

Answer:

$\boldsymbol{f(x) = (x - 4)^2}$