Question

What is the x-value at which the graphs of y = x2 – 2x + 1 and y = x2 + 2x – 7 inter-
sect?

Answer 1

x = 2

Explanation:

Both equations are equal to y, so they're also equal to each other. We then set them equal to each other:

x^2 - 2x + 1 = x^2 + 2x - 7

We now do algebra to isolate x. Subtract 1 from both sides.

x^2 - 2x = x^2 + 2x - 8

Subtract 2x from both sides.

x^2 - 4x = x^2 - 8

Subtract x^2 from both sides.

-4x = -8

Divide both sides by -4.

x = 2