SOLUTION: How do you find a Polynomial that passes through the points (-2,-1) (-1,7) (2,-5), (3,-1)?

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, ).
RELATED QUESTIONS
What polynomial has a graph that passes through the given points (-2, 2) (-1, -1) (1, 5)... (answered by solver91311)

Find the slope (m) of a line that passes through the following points. (m = - 1/7) (4,... (answered by josmiceli)

write an equation of the line that passes through each pair of points. find the slope and (answered by jake_6233)

Find the equation of the line that passes through the points (1,-1) and... (answered by jim_thompson5910)

Find the equation of a line that passes through the points (1,-2) and... (answered by Alan3354)

How do you find the polynomial whose graph goes through these points? (2,10),... (answered by greenestamps,Fombitz)

How do I find the equation for the line that passes through points (-1,5) and (-1,-7)? (answered by Alan3354)

Find an equation of a straight line that passes through point points (3,5) and is... (answered by Fombitz)

What is the slope of line that passes through the points (7,-2) and... (answered by Edwin McCravy)