The parabola whose equation is 5x 2 - y = 12 opens

up

down

left

right

5x^2-y=12

y=5x^2-12

dy/dx=10x

d2y/dx2=10

Since acceleration is constant, which is true of all quadratics, and it is positive, there is an absolute minimum for y (x) when dy/dx=0. So it increases without bound on either side of the vertex, meaning that it opens upwards.