Algebra - Parabolas

Question

Given the equation x^2=-2x+8, the X intercepts are -4 and 2. The equation in the proper quadratic form can be either x^2+2x-8 =0 or -x^2-2x+8=0. in one case the parabola opens up, in the other, it opens down. Which is right and why?

Answer 1

Both equations have the x-intercepts of -4 and 2. (Substitute to confirm.)

Note that -x² - 2x + 8 = -(x² + 2x - 8).