Question

Writing a Polynomial Function of a Graph:

use the fact that the graph passes through (0,36) to find the coefficient a in f(x)=a(x+3)(x+1)(x-2)(x-3)
a=???

Answer 1

we can see that

zeros are at x=-3 , x=2 , x=3

now, we can set up function

`f(x)=a(x+3)(x-2)(x-3)`

now, we can select any one point and then we can find 'a'

(0,36)

x=0 and f(x)=36

we can plug it and then we can find 'a'

`36=a(0+3)(0-2)(0-3)`

`a=2`

now, we can plug it back

and we get

`f(x)=2(x+3)(x-2)(x-3)`

now, we can multiply it

we get

`f(x)=2x^3-4x^2-18x+36`............Answer