How do you write an equation for a parabola that has certain roots?
Matthew Harrington 
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.
$\endgroup$ 61 Answer
$\begingroup$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.
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