Question

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

Explanation:

Step1: Identify x-intercepts

The parabola intersects the x - axis at \(x=-5\) and \(x = - 1\) (from the graph, the roots are at these x - values).

Step2: Use axis of symmetry formula

For a parabola, the axis of symmetry is given by the formula \(x=\frac{x_1 + x_2}{2}\), where \(x_1\) and \(x_2\) are the x - intercepts. Substituting \(x_1=-5\) and \(x_2=-1\) into the formula, we get \(x=\frac{-5+( - 1)}{2}=\frac{-6}{2}=-3\).

Answer:

The equation of the axis of symmetry is \(x = - 3\)