How do you write an equation for a parabola that has certain roots?

Question

The question is

Write a quadratic equation for a parabola that opens downwards and has zeros at $x=4$ and $x = -5$.

I don't even know where to start, any help is greatly appreciated.

Answer 1

If the axis is strictly vertical or parallel to x-axis we have

$$ y= -A (x-4)(x+5) $$

whre $A$ is positive real... when a parabolic shape container spills water or looks downwards.

If the axis is not vertical then parabola

$$ y= a x+b + \sqrt{c x +d} $$

has roots

$$(c-2 a b \pm \sqrt {-4 a b c+c^2+4 a^2 d})/(2 a^2)$$

that is bit more cumbersome to work back.