Question

using the graph, determine the equation of the axis of symmetry.

Explanation:

Step1: Recall the axis of symmetry concept for parabolas

For a parabola, the axis of symmetry is a vertical or horizontal line. In this case, since the parabola opens to the right (as it is a sideways - opening parabola), we use the formula for a parabola of the form \((y - k)^2=4p(x - h)\), and the axis of symmetry is \(y = k\).

Step2: Identify key points on the graph

Looking at the graph, we can observe that the parabola is symmetric about a horizontal line. We can find two points that are symmetric with respect to the axis of symmetry. For example, if we consider two points on the parabola that have the same \(x\) - value (but different \(y\) - values in a symmetric way). Another way is to note that the vertex of the parabola is at \((h,k)\). The vertex of the given parabola is at \((- 2,0)\). For a parabola of the form \((y - k)^2=4p(x - h)\), the axis of symmetry is \(y=k\).

Answer:

\(y = 0\)