The graph shows the axis of symmetry for a quadratic function f(x).

Question

On a coordinate plane, a vertical dashed line at (4, 0) is parallel to the y-axis.
Which could be the function?

f(x) = (x + 4)2
f(x) = x2 + 4
f(x) = (x – 4)2
f(x) = x2 – 4
Mark this and return

Answer 1

The axis of symmetry for a quadratic function in the form \( f(x) = a(x - h)^2 + k \) is given by the line \( x = h \). The dashed vertical line at \( x = 4 \) indicates that the axis of symmetry is at \( x = 4 \).

This means that \( h = 4 \) in the function’s vertex form. Out of the options given, we can analyze each one:

1. \( f(x) = (x + 4)^2 \): The axis of symmetry is at \( x = -4 \) (not 4).
2. \( f(x) = x^2 + 4 \): The axis of symmetry is at \( x = 0 \) (not 4).
3. \( f(x) = (x - 4)^2 \): The axis of symmetry is at \( x = 4 \) (this is correct).
4. \( f(x) = x^2 - 4 \): The axis of symmetry is at \( x = 0 \) (not 4).

Therefore, the only correct option that matches the axis of symmetry at \( x = 4 \) is:

\( f(x) = (x - 4)^2 \).