SOLUTION: i have to find the quadratic function {{{y=ax^2+bx+c}}}whose graph passes through the given points: (-1,6)(1,4)(2,9). I know the "x"s in the quadratic equation will correspond to t

Algebra ->  Linear-equations -> SOLUTION: i have to find the quadratic function {{{y=ax^2+bx+c}}}whose graph passes through the given points: (-1,6)(1,4)(2,9). I know the "x"s in the quadratic equation will correspond to t      Log On


   

Question 378563: i have to find the quadratic function y=ax%5E2%2Bbx%2Bcwhose graph passes through the given points: (-1,6)(1,4)(2,9). I know the "x"s in the quadratic equation will correspond to the x-coordinates in the three ordered pairs, and I also know this will be a quadratic system. I took a stab at it, but I'm doubtful about it. What i have so far is:

6=a%2A-1%5E2%2Bb%2A-1%2Bc
4=a%2A1%5E2%2Bb%2A1%2Bc
9=a%2A2%5E2%2Bb%2A2%2Bc
which i THINK is -ax%5E2%2B-bx%2Bc
ax%5E2%2Bbx%2Bc
2x%5E2%2B2b%2Bc
Ok. that's as far as i got, and it's dubious at best!! Please help! how do i denote the quadratics using the given ordered pairs, then how do i arrive at just one quadratic equation?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you're almost finished

you've generated a system of three equations in a, b, and c

just solve the system for the three values

6 = a - b + c

4 = a + b + c

9 = 4a + 2b + c