In Problems 7780 write a polynomial function whose graph is

In Problems 77-80, write a polynomial function whose graph is shown (use the smallest degree po

Solution

Given polynomila cuts the x axis at two points ie.e x= -4 , x= 3

It touches the x axis at x=-1 ( root of multiplcity 2)

So, f(x) can be written as , f(x) = a(x+1)^2(x+4)(x - 3)

It passes through ( 1, -8)

-8 = a(2^2)(5)(-2)

-8 = a*(-8)*5

a = 1/5

So, f(x) = (1/5)(x+1)^2(x+4)(x - 3)