Question

a polynomial function p of degree 3 contains the points (0,3) (1,1) (2,9) (3,33). find an equation for p.

Answer 1

if they actually do fit on a degree 3, then you only need 3 points to construct it with

Answer 2

make 3 equations with 3 unknowns and solve with your favorite method

Answer 3

\[\begin{array}\ x^3a+x^2b+xd+c=y\\x^3a+x^2b+xd+c=y\\x^3a+x^2b+xd+c=y\\x^3a+x^2b+xd+c=y\\\end{array}\]

hmm, looks like i miscounted to begin with :) for a degree 3 we need 4 points ...

Answer 4

plug in the values for each point into a separate row and then the fastest way would be to row reduce an augmented matrix form it

Answer 5

augmented matrix?

Answer 6

yes, which is a suitable way to obtain the missing values; but it is math level dependant ....

Answer 7

im not at that level yet, how do i start?

Answer 8

well, take the generic set up ive provided and fill in the point values; one row for each point. this will give you a set of 4 equation to play with

Answer 9

what do i do once i have the equations?

Answer 10

substitutions, or eliminations, or any other method of solving a system of equations that you ahve come across and are confident in using .... there is no single way to approach this.

Answer 11

that (0,y) point will provide you a useful way to knock this down to a system of 3 equations right off the bat

Answer 12

0a + 0b + 0c + d = 3 ; therefore d=3 can be reused on the others and we are down to 3 equations to solve for