Question

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

Answer 1

Given function: $y=x^3 + 6x^2 + 8x$

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:

x⇒∞, y⇒∞

x⇒-∞, y⇒-∞

Answer 2

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

as $x \to \infty , y\to \infty$

as $x\to -\infty, y \to -\infty$

For better understanding see the graph.

Step-by-step explanation:

Given :

$y = x^3 + 6x^2 +8x$

$y=x(x^2+6x+8)$

$y = x(x^2+4x+2x+8)$

$y=x(x(x+4)+2(x+4))$

$y=x(x+4)(x+2)$

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 $x \to \infty , y\to \infty$

as $x\to -\infty, y \to -\infty$

For more information, refer the link given below

https://brainly.com/question/20104762?referrer=searchResults