Write the equation of a parabola with a vertex at (0,0), a focus at (2,0), and directrix x=-2

The directrix is x=-2, which means the parabola opens horizontally instead of vertically. The equation is (y - k) ² = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p

in this case, h+p=2, k=0, and h-p=-2

solve for h and p: h=0, p=2

plug the numbers into the equation: (y-0) ²=4*2 (x-0)

simplify: y²=8x