Question

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

Explanation:

Step1: Identify x-intercepts

The parabola intersects the x - axis at \(x=-8\) and \(x = - 6\).

Step2: Calculate midpoint

The formula for the axis of symmetry of a parabola (a vertical line) when we know two x - intercepts \(x_1\) and \(x_2\) is \(x=\frac{x_1 + x_2}{2}\). Substituting \(x_1=-8\) and \(x_2=-6\), we get \(x=\frac{-8+( - 6)}{2}=\frac{-14}{2}=-7\).

Answer:

The equation of the axis of symmetry is \(x = - 7\)