Question

How can I tell whether a parabola opens upward or downward?

Answer 1

The highest order term, the coefficient of the `x^2` term, will tell you. Or, graphically, if it looks like a bowl instead of a mountain.

Explanation:

Though any quadratic formula will 'dip' one way or another, the term that will provide the strongest overall direction to the equation will be the 'leading term', or the term with the highest power.

If the term is positive, then as `x^2` dominates the `x` term with bigger values of `|x|`, the result of the equation will become bigger and bigger.