Suppose the equation of the axis of symmetry for a quadratic function is x = 3
and one of the x-intercepts is 8.
What is the other x-intercept?
Recognize that the graph of this function will be symmetric with respect to the axis of symmetry, which is x=3. If one x-intercept is 7, we can quickly calculate that this intercept is 4 units from that axis. The other x-intercept is 4 units from that axis, but in the other direction; therefore, it is x=3-4 = -1.