Question

using the graph, determine the equation of the axis of symmetry.
answer
answer type
two points
one point
one equation

Explanation:

Step1: Identify the x-intercepts

From the graph, the parabola intersects the x - axis at \(x=-5\) and \(x = - 3\) (assuming the points are at these x - values, we can see the symmetry around the mid - point of these two x - intercepts).

Step2: Calculate the mid - point

The formula for the mid - point between two x - values \(x_1\) and \(x_2\) is \(x=\frac{x_1 + x_2}{2}\). Here, \(x_1=-5\) and \(x_2=-3\). So \(x=\frac{-5+( - 3)}{2}=\frac{-8}{2}=-4\). The axis of symmetry of a parabola is a vertical line (since the parabola opens downwards or upwards) in the form \(x = h\), where \(h\) is the x - coordinate of the vertex (or the mid - point of the x - intercepts for a parabola that intersects the x - axis at two points). So the equation of the axis of symmetry is \(x=-4\).

Answer:

The equation of the axis of symmetry is \(x = - 4\)