Find the standard form of the equation of a parabola (centered at the origin) that passes through the point (-2, 4) with a horizontal axis.

The axis of the parabola is horizontal. The standard form of
a parabola centered at the origin is y^{2}=4px, where h=0, k=0. We also
know that the parabola passes through the point (-2, 4) – so we can plug in
x=-2 and y=4 to find p.

y^{2}=4px , (4)^{2}=4p(-2), 16=-8p,-2=p

Therefore, the equation of the parabola with h=0, k=0, and p=-2 is

y^{2}=4px, y^{2}=4(-2)x, y^{2}=-8x