Question

How do you know if a parabola opens up or down $?$

Answer 1

To find out if parabola open upwards or downwards:

If the leading coefficient of a quadratic function is greater than zero $a>0$ , the parabola opens upward.

If the leading coefficient of a quadratic function is less than zero, $a<0$ , the parabola opens downward.

For example:

The parabola of equation $y=4x^2$ open upwards and the parabola of equation $y=-4x^2$ open downwards.

Hence, with the help of leading coefficient $a$ we can determine if parabola opens up or down.