Question

What determines whether a parabola will open up or down

Answer 1

If the coefficient of the leading term is positive, it opens up. If the coefficient of the leading term is negative, it opens down. The leading term is the ax^2 term.

Answer 2

A parabola will usually have an equation like y= -2x^2 + 3x +2 (2x squared) What determines whether it is up or down is the sign of the coefficient of the x squared term in this case it is -2. If the sign of the coefficient is negative then it the open part of the parabola will be facing down.