Mathematics, 18.07.2019 19:00 mariaceleste110505

Which is the graph of the function f(x) = x3 + 6x2 + 11x + 6?

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Answer from: SmoothCruzito16

The graph of the function is attached below.

The roots of the given equation are -3, -2, and -1.

We have to determine the graph of the function f(x) = x3 + 6x2 + 11x + 6.

According to the question,

The graph of the function is determined by factorizing the function following all the steps given below.

$\rm f(x) = x^3 + 6x^2 + 11x + 6.$

Factorize the equation,

$\rm x^3 +6x^2+ 11x + 6\\\\ x^3+3x^2+3x^2 + 9x+2x+ 6\\\\ x(x^2+3x+2) +3(x^2+3x+2)\\\\(x+3) (x^2+3x+2)\\\\(x+3) (x+1) (x+2)$

The roots of the equation are as follows;

$\rm x+3=0, \ \ x=-3\\\\x+2=0,\ \ x=-2\\\\x+1=0, \ \ x=-1$

Hence, the roots of the given equation are -3, -2, and -1.

To know more about the Cubic equation following all the steps given below.

link

Answer from: demetriascott20

f(x) = x^3 + 6x2 + 11x + 6 begins with a positive 3rd power of x. Immediately we know that the graph begins in Quadrant 3 and continues (not ends) in Quadrant 1. Looking at the last term, we see that possible factors may be 6, 3, 2 or 1 or one or more of the negatives. Supposing I chose -2 and test whether it is or is not a root of this function:

_____________
-2 / 1 6 11 6
-2 -8 -6
----------------------
1 4 3 0

Because the remainder here is zero, we know that -2 is a root. Thus, the graph passes thru (-2,0). From the coefficients 1 4 3, we see that -1 and -3 are the other roots. The graph crosses the x-axis at x = -1, x= -3 and x= -2.
Can you now identify the graph that properly represents f(x) = x3 + 6x2 + 11x + 6?
Which is the graph of the function f(x) = x3 + 6x2 + 11x + 6?

Which is the graph of the function f(x) = x3 + 6x2 + 11x + 6?

Answer from: Quest

answear:

step-by-step explanation: a

Answer from: Quest

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

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