Write the Quadratic...

[dsheller]

Find the quadratic function that goes through the points ( 0, f(0) ), (deltax, f(deltax) ), ( 2deltax, f(2deltax) ). In other words find the values of a, b, and c such that those points satisify the equation g(x) = ax^2 + bx + c. Hint g(0) = f(0)

Alright, i'm not getting how to do this at all, can anyone lead me in the right direction?

[VBAhack]

Find the quadratic function that goes through the points ( 0, f(0) ), (deltax, f(deltax) ), ( 2deltax, f(2deltax) ). In other words find the values of a, b, and c such that those points satisify the equation g(x) = ax^2 + bx + c. Hint g(0) = f(0)

Alright, i'm not getting how to do this at all, can anyone lead me in the right direction?

Since 3 non-colinear points uniquely determine a parabola, I think the approach is straightforward. What you are trying to do is find a,b,c:

y = ax² + bx + c

given three points (x₁,y₁), (x₂,y₂), (x₃,y₃)

Thus, you have

(1)... y₁ = ax₁² + bx₁ + c
(2)... y₂ = ax₂² + bx₂ + c
(3)... y₃ = ax₃² + bx₃ + c

These are 3 equations in 3 unknowns (a, b, c) and by substitution you can obtain expressions for the unknowns in terms of x₁, y₁, x₂, y₂, x₃, y₃. Hint: the fact that x₁ = 0 makes things much easier.

Good luck.