Question

The equation for a parabola has the form y = ax2 + bx + c, where a, b, and c are constants and a ≠ 0. find an equation for the parabola that passes through the points (−1, −10), (1, −6), and (2, −13).

Answer 1

To solve the problem, substitute the given points for x in the given equation to get

$-10=(-1)^2a+(-1)b+c\Rightarrow-10=a-b+c \\ -6=(1)^2a+(1)b+c\Rightarrow-6=a+b+c \\ -13=(2)^2a+(2)b+c\Rightarrow-13=4a+2b+c$

Solving the three equations simultaneously, we have:

a = -3, b = 2 and c = -5

Therefore, the required equation is

$y=-3x^2+2x-5$