Given that f(x) is a quadratic function and that f(x) is only positive when x lies between -1 and 3, find f(x) if f(-2) = -10.

Question

What i did:

$f(x)=ax^2+bx+c$

$f(-2)=4a-2b+c=-10$

$f(0) =c > 0$

$f(1) =a+b+c > 0$

$f(2) =4a+2b+c > 0$

I thought using $b^2-4ac = 0$ for $f(-2)$ but its wrong since I am getting c = -6.

ANS: $-2x^2+4x+6$

Answer 1

So $-1$ and $3$ are zeroes of this function so we can write it in factor form:

$$ f(x)=a(x+1)(x-3)$$ Now use $f(-2)=10$ to get $a$.