System of Linear Equations + Quadratic Functions problem

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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!

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$$a-b+c=6$$ $$a+b+c=4$$ $$4a+2b+c=9$$

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 $b$.