Question 906001: How do you find a Polynomial that passes through the points (-2,-1) (-1,7) (2,-5), (3,-1)?
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! Infinitely many polynomials can contain those four points. Pick as low a degree function as you can.
A root occurs between x at -2 and -1.
A root occurs between x at -1 and 2.
We do not expect a root between x at 2 and 3.
The function f may be degree 3 with a positive leading coefficient. From -1 to 2, f decreases, and from 2 to 3, f increases.
 can be the general form for the cubic equation, and specific equations can be made from each of the four given points. Setup a system of equations and solve for a, b, c, and d.
Simplify the equations; Solve the system any way you know.
(Yes, those are FOUR different equations, but they are a SYSTEM OF EQUATION. They are linear in the variables, a, b, c, d. They are based on the a general form from the cubic equation which is still unknown, ).
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