Question

The axis of symmetry of a parabola is the line x = 4.

(a) Suppose that one x-intercept is 10; what is the other one?
(b) Suppose the point (12, 4) is on the graph; what other point also must be on the graph?

Answer 1

(-2, 0) and (-4, 4)

Explanation:

Since we know that in a parabola, the axis of symmetry is in the exact middle of the x-ints, we can find the x-intercept quickly. Since the x-int is 10, and the axis is at 4, we know the distance from the axis to the intercept is 6. This means that if we do 4-6, we will get the other x-int, which is -2, so the other x-int is (-2,0).

reflect the first point (12, 4) around the axis x = 4

the other point is at a distance z from the axis of symmetry:

z = 12 - 4 = 8

but on the other side of the axis:

x= 4-z

x = 4 - 8

x = -4

so the other point is (-4, 4)