What is the equation of a parabola that goes through points (0,1), (–1,6),and (2,3)?
Substitute the given points into the model $\displaystyle y = ax^2 + bx + c$:
$\displaystyle (0, \, 1) \Rightarrow 1 = c$.
Update the model:
$\displaystyle y = ax^2 + bx + 1$.
$\displaystyle (-1, \, 6) \Rightarrow 6 = a - b + 1 \Rightarrow a - b = 5$ .... (1)
$\displaystyle (2, \, 3) \Rightarrow 3 = 4a + 2b + 1 \Rightarrow 2a + b = 1$ .... (2)
Solve equations (1) and (2) simultaneously.