Question

a quadratic function is shown below.
what is the axis of symmetry of the quadratic function?
○ $y = 4$
○ $y = -9$
○ $x = -9$
○ $x = 4$

Explanation:

Step1: Recall axis of symmetry property

The axis of symmetry of a parabola (quadratic function) is a vertical line (since parabola opens up/down) in the form \( x = h \), where \( h \) is the x - coordinate of the vertex. From the graph, the vertex lies on the vertical dashed line. By observing the grid, the x - coordinate of the vertex (where the parabola changes direction) is 4. So the axis of symmetry is a vertical line \( x = 4 \). Also, we can eliminate options with \( y=\) (since axis of symmetry for vertical parabola is vertical, so equation is \( x=\) some value) and \( x = - 9\) (doesn't match the vertex's x - coordinate).

Step2: Identify correct option

Among the given options, the axis of symmetry is \( x = 4 \) as it is a vertical line passing through the vertex of the parabola.

Answer:

D. \( x = 4 \)