Question

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

Explanation:

Step1: Recall axis of symmetry rule

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

Step2: Identify axis from graph

Graph shows axis $x=4$, so $h=4$.

Step3: Match to options

Find function with $h=4$.

Answer:

C. $f(x) = (x - 4)^2$