Question

Part A

Describe the type of function shown in the graph.
Part B
What are the standard form and the factored form of the function?

Answer 1

A

`F(x)=-(1)/(1500)(x+20)(x+5)(x-15)`

B

`=> F(x)=-(x^3)/(1500)-(x^2)/(150)+(11x)/(60)+1`

Explanation:

Function and its graphs

Part A

The graph shown in the image corresponds to a cubic function because of its classical infinite branches, three real roots and two extrema values

Part B

Knowing the value of the three roots x=-20, x=-5, and x=15 we can express the cubic function in factored form:

`F(x)=C(x+20)(x+5)(x-15)`

The value of C will be determined by using any particular point from the graph. Let's use (0,1)

`1=C(0+20)(0+5)(0-15)`

`C=-(1)/(1500)`

Replacing, we find the factored form of the function

`F(x)=-(1)/(1500)(x+20)(x+5)(x-15)`

The standard form demands to expand all the products and simplify

`F(x)=-(1)/(1500)(x^3+10x^2-275x-1500)`

`=> F(x)=-(x^3)/(1500)-(x^2)/(150)+(11x)/(60)+1`