Question

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

Explanation:

Step1: Identify x-intercepts

The graph intersects the x - axis at \(x=-6\) and \(x = - 2\).

Step2: Use midpoint formula

The formula for the midpoint of two points \(x_1\) and \(x_2\) is \(\frac{x_1 + x_2}{2}\). Substituting \(x_1=-6\) and \(x_2=-2\), we get \(\frac{-6+( - 2)}{2}=\frac{-8}{2}=-4\). The axis of symmetry of a parabola (the graph is a parabola) is a vertical line passing through the midpoint of its x - intercepts (or the vertex), so the equation of the axis of symmetry is \(x=-4\).

Answer:

\(x = - 4\)