SOLUTION: Find a polynomial function whose graph passes through each set of points. (-2,10) (-1,-4) (0,-2) (1,-2)

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Question 1063017: Find a polynomial function whose graph passes through each set of points. (-2,10) (-1,-4) (0,-2) (1,-2)
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Four points could go well for degree-three polynomial function.
Unknown constant coefficients, a, b, c, d;
ax%5E3%2Bbx%5E2%2Bcx%2Bd=y

Use the given points to form four specific degree-three equations for a system.




system%28-8a%2B4b-2c%2Bd=10%2C-a%2Bb-c%2Bd=-4%2Cd=-2%2Ca%2Bb%2Bc%2Bd=-2%29
This is the system to solve.


Substituting for d makes for a simpler three-variable system
system%28-8a%2B4b-2c=12%2C-a%2Bb-c=-2%2Ca%2Bb%2Bc=0%29

(-1/2)*E1 gives
system%284a-2b%2Bc=-6%2Ca-b%2Bc=2%2Ca%2Bb%2Bc=0%29

E1-E3 and E2-E3 give
system%283a-3b=-6%2C-2b=2%29

system%28a-b=-2%2Cb=-1%29

This very simple system gives two of the variables.
highlight%28system%28b=-1%2Ca=-3%29%29

d was already found early, and with a, b, d, all now found, c can be evaluated, whichever equation you want.

highlight%28system%28a=-3%2Cb=-1%2Cc=4%2Cd=-2%29%29