Two parabolas are the graphs of the equations $y=2x^2-10x-10$ and $y=x^2-4x+6$.. Give all points where they intersect. List the points in order of increasing $x$-coordinate, separated by semicolons.
To solve this, set the functions equal
2x^2 - 10x - 10 = x^2 - 4x + 6 rearrange as
x^2 - 6x - 16 = 0 factor as
(x - 8) ( x + 2) = 0
Setting each factorto 0 and solving for x, we have that x = 8 and x = -2
So....using x^2 - 4x + 6 we can find the two y values
(-2)^2 -4(-2) + 6 = 18 ⇒ (-2, 18)
8^2 - 4(8) + 6 = 38 ⇒ (8, 38)