stefan88 wrote:its obvisously 3rd order and i know the leading coefficient is 1...so have x^3 + bx^2 + cx + d = F(x)
can anyone hint as to how to go about it?
Just as a quadratic (a polynomial of degree two) is uniquely determined by three points, so also a cubic (a polynomial of degree three) is uniquely determined by four points.
So pick any four of the given points, and plug them into the cubic's equation. I like smaller values, so I'd probably pick (-1, 0), (0, -6), (1, -8), and (2, 0):. . . . .
-1 + b - c + d = 0. . . . .
d = -6. . . . .
1 + b + c + d = -8. . . . .
8 + 4b + 2c + d = 0
Then solve the system of equations
for the values of the coefficients. P.S. Alternatively, you could plug all of the points into a graphing calculator in "STAT" mode, and do the cubic regression. You will discover that your impulse was
exactly right: this doesn't just
look like a cubic; it
is a cubic