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 y2=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.
y2=4px , (4)2=4p(-2), 16=-8p,-2=p
Therefore, the equation of the parabola with h=0, k=0, and p=-2 is
y2=4px, y2=4(-2)x, y2=-8x