Question

Consider the equations g(x) = x^2 – 2x – 10 and h(x) = -x^2 - 6x + 6. Use algebra to

find the coordinates of the intersection of the two parabolas.​

Answer 1

Explanation:

At the point of intersection of these two curves, g(x) = h(x). Setting the two functions equal to each other, we get:

x^2 - 2x - 10 = -x^2 - 6x + 6

Grouping like terms on the left side, we get:

2x^2 + 4x - 16 = 0

Simplifying by dividing all four terms by 2, we get:

x^2 + 2x - 8 = 0, or (after factoring) (x - 2)(x + 4) = 0.

Then x = 2 or x = -4.

The y-value for x = 2 is g(2) = 2^2 - 2(2) - 10, or -10, and so this point of intersection is (2, -10).

The y-value for x = -4 is g(-4) = (-4)^2 - 2(-4) - 10, or 16 + 8 - 10, or 14, and so this point of intersection is (-4, 14).