Give an example of 2 different possible polynomial functions

Give an example of 2 different possible polynomial functions whose graph is shown below:

Solution

root at x = -1 ( multplicity 2 as it touches the graph)

x = 1 ;

root at x = 2 ( multplicity 2 as it touches the graph)

Its an odd polynomial with degree =5 ; ends in opposite direction.

f(x) ---> inf +ve ; x .---> -inf

f(x) ---> inf -ve ; x .---> +inf

highest polynomial -ve

f(x) = a(x +1)^2(x -1)(x -2)^2

y interept : ( 0, 4)

4 = a(1)(-1)(2)^2 ; a = -1

f(x) = -(x+1)^2(x -1)(x -2)^2

 Give an example of 2 different possible polynomial functions whose graph is shown below: Solutionroot at x = -1 ( multplicity 2 as it touches the graph) x = 1

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