Suppose that the graph of f(x) is a parabola intersecting the origin and containing the points (-2,8) and (-3,6). Find f(x).

I think i start by setting the equation. A parabola is a quadratic eq. so id use ax^2+bx+c. Noticing that it intersects thru the origin, 0 is the y-in so its just ax^2+bx. Next I plug in the points -2,8 into the equation and do the same for -3,6 to get 2 diff. equations:

8=a(-2)^2+b(-2)

8=4a-2b

8-2b=4a

a=(8-2b)/4

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6=a(-3)^2+b(-3)

6=9a-3b

6-9a=-3b

(6-9a)/-3=b

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Im not sure if im right so far, or how to proceed. Any ideas?

Thanks.