I'm having trouble finding the coefficients in this equation based on knowing where a parabola passes through at certain points.
Question:
By solving a system of $3$ equations in $3$ variables, find the coefficients in the equation of the parabola $y = \alpha + \beta x + \gamma x^2$ that passes through the points $(1, 1)$, $(2, 2)$ and $(3, 0)$.
you have $$a+b+c=1$$ $$4a+2b+c=2$$ $$9a+3b+c=0$$ multiplying the first by $-4$ and adding to the second we get $$2b+3c=2$$ (I) multiplying the first by $$-9$$ and adding to the last one we get $$6b+8c=9$$ (II) multiplying $(I)$ by $-3$ and adding to (II) we get $$-c=3$$ can you proceed?