Question

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

Explanation:

Step1: Identify the vertex's x - coordinate

The axis of symmetry of a parabola is a vertical line that passes through the vertex of the parabola. From the graph, we can see that the vertex of the parabola (the highest point of the parabola) has an x - coordinate of - 6.

Step2: Determine the equation of the axis of symmetry

For a vertical line, the equation is of the form \(x = a\), where \(a\) is the x - coordinate of any point on the line. Since the axis of symmetry passes through the vertex with \(x=-6\), the equation of the axis of symmetry is \(x=-6\).

Answer:

\(x = - 6\)