Question

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

Answer 1

Many answers possible:
Ex. `y = 2x^2 - 50` opens up and `y = -24x^2 + 600` opens down

Explanation:

The form `y = c(x - a)(x - b)` 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(x - 5)(x + 5)`
`y = 2(x^2 - 25)`
`y = 2x^2 - 50` opens up

AND

`y = -24(x -5)(x + 5)`
`y = -24(x^2 - 25)`
`y = -24x^2 + 600` opens downwards

Hopefully this helps!