How do I tell if a parabola has a minimum or a maximum?

Question

asked Jul 28, 2023 111k views

1 Answer

Adam Lukaszczyk · Answer 1 · 2023-08-04T01:53:17+0000

We can write the equation of a parabola in two different ways:

The standard form:

$\begin{gathered} y=ax^2+bx+c \\ a\\e0 \end{gathered}$

And the vertex form:

If the parabola has a minimum or a maximum depends on the leading coefficient (the coefficient of x²) or in both cases the coefficient a.

Let's see the cases:

$a>0_{\text{ }}(a_{\text{ }}is_{\text{ }}positive)$

If a is positive, the parabola opens upwards, so the parabola has a minimum.

$a<0_{\text{ }}(a_{\text{ }}is_{\text{ }}negative)$

If a is negative, the parabola opens downwards, so the parabola has a maximum