Question

How do you know if a parabola is positive or negative $?$

Answer 1

Finding if a parabola is positive or negative:

If the parabola opens to the right or in the upward direction, then the parabola is positive.

If the parabola opens to the left or in the downward direction, then the parabola is negative.

For example:

The parabola of equation $y=4x^2+2x+3$ opens upward as $4>0$ so the parabola is positive and the parabola of equation $y=-4x^2+2x+3$ opens downward as$-4<0$ so the parabola is negative.

Hence, with the help of leading coefficient $a$ we can determine if parabola is positive or negative .