Find the quadratic function y+ax^2+bx+c whose graph passes through the given points:
- (-1,6)
- (1,4)
- (2,9)
I've attempted this on my own, but when cancelling out one variable, I usually end up cancelling more than one which completely throws me off. Any help is appreciated!
$$a-b+c=6$$ $$a+b+c=4$$ $$4a+2b+c=9$$
Adding the first 2 equations, we have $$2a+2c=10$$.
Times $2$ to the first equation and add to the third equations, we have $$6a+3c=21$$
Dividing by $3$, $$2a+c=7$$.
Solving $2a+c=7$ and $2a+2c=10$, we have $c=3$. Now solve for $a$ and $b$.