SOLUTION: Applications and Extensions Curve Fitting. Find the function y=ax^2+bx+c whose graph contains the points (1,2), (-2,-7), and (2,-3)

Question 1058212: Applications and Extensions
Curve Fitting. Find the function y=ax^2+bx+c whose graph contains the points (1,2), (-2,-7), and (2,-3)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Substitute the points into the equation
a+b+c=2
4a-2b+c=-7
4a+2b+c=-3
Look at the second and third
4a=2b-c-7
4a=-2b-c-3
Set those two equal to each other
2b-c-7=-2b-c-3
4b=4
b=1
Now go back to the first and substitute into one of the others.
a+1+c=2 or a+c=1, c=1-a
4a-2+1-a=-7 or 3a=-6, a=-2
Substitute that into the first equation.
-2+1+c=2; c=3
{-2,1,3}
-2x^2+bx+3=y answer
Try each point
-2+1+3=2 CHECKS
-8-2+3=-7 CHECKS
-8+2+3=-3 CHECKS

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