Parabola through three points

Find the parabola through the three points $(0, 1)$, $(1, 0)$, and $(2, 3)$. Write it as $y = ax^2 + bx + c$ and substitute each point. From $(0, 1)$, $c = 1$; from $(1, 0)$, $a + b + c = 0$; from $(2, 3)$, $4a + 2b + c = 3$.

Using $c = 1$ leaves $a + b = -1$ and $2a + b = 1$; subtracting gives $a = 2$ and $b = -3$. Hence $y = 2x^2 - 3x + 1$. The large dots mark the three points, and the parabola passes through all of them.