Function Notations for quadratics

Question

Given $T(x) = ax^2 + bx + c$ Find $a,\,b$ and $c$ if $T(0) = -4$, $T(1) = -2$ and $T(2) = 6$

I first made $C$ for when $x = 0,\,-4$. But don't know were to go from here. Any help?

Answer 1

Since $c=-4$, it follows $T(1)=a+b-4$ and $T(2)=4a+2b-4$. Also, you know $T(1)=-2$ and $T(2)=6$. You must find $a$ and $b$ satisfying \begin{align*} a+b-4&=-2\\ 4a+2b-4&=6 \end{align*}

Answer 2

Hint: $T(1) = a+b+c$, and $T(2) = 4a+2b+c$, but $c = T(0) = -4$. Can you finish it off...?