Find the equation of the parabola y = ax² + bx + c that contains the points (1, -2), (2, 0), and (4, 22).
Plug in the points and you'll get three equations.
$\displaystyle a+b+c = -2$
$\displaystyle 4a+2b+c = 0 $
$\displaystyle 16a+4b + c = 22 $
You can solve this system of equations in a number of ways. I recommend setting up a matrix.
$\displaystyle \bigg(\begin{array}{ccc}
1 & 1 & 1 \\
4 & 2 & 1 \\
16 & 4 & 1 \end{array}\bigg) \bigg( \begin{array}{ccc}
a \\
b \\
c \end{array}\bigg) = \bigg(\begin{array}{ccc}
-2 \\
0 \\
22 \end{array} \bigg)$
So let's write that as $\displaystyle AX = B $. We want to find x, hence: $\displaystyle X = BA^{-1} $
And you know how to calculate the inverse of a 3x3 matrix hopefully! $\displaystyle A^{-1} = \frac{adj(A)}{det(A)} $