Question

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

Explanation:

Step1: Identify x-intercepts

The parabola intersects the x - axis at \(x=-7\) and \(x = - 3\).

Step2: Use axis of symmetry formula

The formula for the axis of symmetry of a parabola (for a quadratic function) when we know the x - intercepts \(x_1\) and \(x_2\) is \(x=\frac{x_1 + x_2}{2}\).
Substitute \(x_1=-7\) and \(x_2=-3\) into the formula: \(x=\frac{-7+( - 3)}{2}=\frac{-10}{2}=-5\).

Answer:

The equation of the axis of symmetry is \(x = - 5\)