Graph y=x^3 + 6x^2 + 8x and describe the end behavior

The graph attached below we can clearly see the end behaviour,

as

as

For better understanding see the graph.

Step-by-step explanation:

Given :

Therefore, we got x-intercepts (0,0), (-2,0) and (-4,0).

From the graph attached below we can clearly see the end behaviour,

as

as

For more information, refer the link given below

link

Given function:

In order to graph it, let us find some coordinates for the given function to plot on graph.

Let us find the x-intercepts first by setting given function equal to 0.

x^3 + 6x^2 + 8x =0.

Factoring out x.

x(x^2+6x+8) = 0

Factoring quadratic x^2 +6x +8, we get

x(x+2)(x+4) =0

Applying zeros product rule, we get

x =0

x+2 = 0  => x = -2

x+4 =0  => x = -4.

Therefore, we got x-intercepts (0,0), (-2,0) and (-4,0).

Because degree is 3 and leading coefficient a positive number, the graph would go down on the left and go up on the right.

From the graph we can see end behaviour:

g(x) is the negative form of f(x)? because whenever its the negative form it reflects its self over the x axis. idk if this is right though.

step-by-step explanation:

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2