Question

Find a polynomial function if Y-intercept is `(0,-4)`. The X-intercepts are `(-2,0)` and `(2,0)`. Degree is `2`. End behaviour is `xrarr-oo,f(x)rarroo` and `xrarroo,f(x)rarroo` ?

Answer 1

`x^2-4`

Explanation:

Degree 2 and zeros `-2` and `2` tells us

`f(x) = a(x+2)(x-2) = a(x^2-4)`

`f(0) = -4` gets us `a = 1`,

so `f(x) = x^2-4`