Quadratics: Solve for B and C. If I know that the points (-1,6) and (2,3) are on the graph of the quadratic function f(x) = 2x^2 + bx + c, how do I determine b and c?
Thanks to anyone who helps.

Use the given points.. (-1,6) & (2,3) 
You know that the function will become 6 when $x$ is (-1) and it will become 2 when $x$ is 3
In other words$$f(-1) = 6$$ $$f(2) = 3 $$
 that data leads you to 2 different equations as

$$6 = 2(-1)^2 + (-b) + c $$ $$3 = 2(2)^2 + 2b + c $$

now solving the system of equation is all that remaining... its all up to u :)
