Question

what is the equation for the axis of symmetry for the function shown on the graph?

Explanation:

Step1: Identify parabola's form

The graph shows a parabola opening to the left. For a parabola of the form \(x = ay^{2}+by + c\), the axis of symmetry is a horizontal line.

Step2: Recall axis - of - symmetry formula

For a parabola \(x = ay^{2}+by + c\), the equation of the axis of symmetry is \(y=-\frac{b}{2a}\). For a parabola opening left - right, the axis of symmetry passes through the vertex. By observing the graph, the vertex of the parabola has a \(y\) - coordinate of \(0\). So the equation of the axis of symmetry is \(y = 0\).

Answer:

\(y = 0\)