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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=???

Writing a Polynomial Function of a Graph use the fact that the graph passes through 036 to find the coefficient a in fxax3x1x2x3a class=

Respuesta :

we can see that

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

now, we can set up function

[tex]f(x)=a(x+3)(x-2)(x-3)[/tex]

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'

[tex]36=a(0+3)(0-2)(0-3)[/tex]

[tex]a=2[/tex]

now, we can plug it back

and we get

[tex]f(x)=2(x+3)(x-2)(x-3)[/tex]

now, we can multiply it

we get

[tex]f(x)=2x^3-4x^2-18x+36[/tex]............Answer

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