Question

A polynomial function p of degree 3 contains the points (0, –4), (1, 5), (2, 24), and (3, 59).
Find an equation for p

Answer 1

\[p(x)=ax^3+bx^2+cx+d\]

so this is a problem of interpolation:

\[p(0)=-4\]
\[p(1)=5\]
Can you do the missing ones?

Answer 2

yes, Thank you :)

Answer 3

very good!

Answer 4

but then how do put them into the equation for p?

Answer 5

well it will give you a 4x4 system with a,b,c,d. Solve for them and then plug back into the original equation p(x). That will give you the solution of a polynomial that has the desired characteristics.

Answer 6

It will also give you some easy ones, p(0)=-4 leads to d=-4

Answer 7

So you're actually left with a 3x3 system out of that.