Question

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

Explanation:

Step1: Identify the vertex's x - coordinate

The graph is a parabola (quadratic function graph). The axis of symmetry of a parabola passes through its vertex. From the graph, the vertex (the minimum point of the parabola) has an x - coordinate of - 6.

Step2: Determine the equation of the axis of symmetry

For a vertical parabola (opening up or down), the equation of the axis of symmetry is a vertical line of the form \(x = h\), where \(h\) is the x - coordinate of the vertex. Since the x - coordinate of the vertex is - 6, the equation of the axis of symmetry is \(x=-6\).

Answer:

\(x = - 6\)