# How do you find two quadratic function one that opens up and one that opens downward whose graphs have intercepts (-5,0), (5,0)?

Jan 7, 2017

Ex. $y = 2 {x}^{2} - 50$ opens up and $y = - 24 {x}^{2} + 600$ opens down

#### Explanation:

The form $y = c \left(x - a\right) \left(x - b\right)$ represents intercept form, where $c$ is a constant. If $c > 0$, the parabola opens up. If $c < 0$, the parabola opens down.

So, we can pick absolutely any value of $c$ that is below $0$ if we want the parabola to open down and absolutely any value of $c$ that is above $0$ if we want the parabola to open up.

Thus, we can have equations:

$y = 2 \left(x - 5\right) \left(x + 5\right)$
$y = 2 \left({x}^{2} - 25\right)$
$y = 2 {x}^{2} - 50$ opens up

AND

$y = - 24 \left(x - 5\right) \left(x + 5\right)$
$y = - 24 \left({x}^{2} - 25\right)$
$y = - 24 {x}^{2} + 600$ opens downwards

Hopefully this helps!