Question

Part A

Answer 1

Answer:

A

$F(x)=-\frac{1}{1500}(x+20)(x+5)(x-15)$

B

$=> F(x)=-\frac{x^3}{1500}-\frac{x^2}{150}+\frac{11x}{60}+1$

Step-by-step 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)

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

$C=-\frac{1}{1500}$

Replacing, we find the factored form of the function

$F(x)=-\frac{1}{1500}(x+20)(x+5)(x-15)$

The standard form demands to expand all the products and simplify

$F(x)=-\frac{1}{1500}(x^3+10x^2-275x-1500)$

$=> F(x)=-\frac{x^3}{1500}-\frac{x^2}{150}+\frac{11x}{60}+1$