Question

What is the equation of the parabola with axis intercepts of `x=2`, `x=-4`, and `y=4`?

Answer 1

`y = -1/2x^2-x+4`

Explanation:

The `x` intercepts (`x=2` and `x=-4`) are the zeros of the quadratic function, corresponding to linear factors `(x-2)` and `(x+4)`.

So our equation can be written something like:

`y = a(x-2)(x+4)`

for some constant `a` to be determined.

Putting `x=0` and `y=4`, we have:

`color(blue)(4) = a(color(blue)(0)-2)(color(blue)(0)+4) = -8a`

Hence `a=-1/2` and we have:

`y = -1/2(x-2)(x+4) = -1/2(x^2+2x-8) = -1/2x^2-x+4`