Mathematics, 02.12.2019 05:31 lm942747

Pls hurry! 15 pts!

consider the function f(x)=x^3+2x^2-3. (a) graph the function. (b) what are the x- and y-intercepts of the graph? be sure to answer (a) & (b). also pls show work!

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Answer from: christyr2002

x-intercept = 1 and y-intercept = -3

Step-by-step explanation:

The graph of the function is attached with this answer.

I have used some computer program to draw graph but you can draw a rough graph manually on a graph sheet. For that

first of all you need to know basic structure of a cubic polynomial * which is somewhat like a wave (you can have a look at the graph attached to know the basic structure).Then plot some important points which are point of local maxima ** and local minima ***, point of intercepts (which is the second part of the question - has to be done first in order to draw a more accurate rough diagram of the function).

To Calculate Some Important Points :

Local Maxima and Minima :

These are the points where the the first derivative of the function becomes zero. This means that at these points the graph takes turn, if it was increasing behind this point then it will start decreasing after this point or the other way. The second derivative of the function at these points are either positive or negative (positive for local minima and negative for local maxima).

Intercepts :

To calculate the x-intercept, first you need to analyse the graph to know how many x-intercepts are there. According to this graph only one intercept is there, it means that only one real root of this cubic equation is there (a cubic equation has 3 roots in which either one is real and two are imaginary or all the three are real). To calculate roots of a cubic equation there is no specific way. Generally, the first root is through hit and trial method. So, let's start with the simplest number which is x=0

$(0)^{3}+2(0)^{2}-3 \neq 0$

∴ 0 is not a root.

Now, let x=1

$(1)^{3}+2(1)^{2}-3=0$

∴ 1 is a root.

Since 1 is the only real root of the equation, therefore (1,0) is the only x-intercept of the graph.

To calculate y-intercept, simply put x=0 in the equation which is

$f(0)=(0)^{3}+2(0)^{2}-3=-3\\\therefore f(0)=-3$

Therefore the y intercept is (0,-3).

* Cubic Polynomial : Polynomials which have a degree (highest power of the variable) of 3 are called cubic polynomials.

** Local Maxima : Points at which the left and right neighbours have less function value are called local maxima.

*** Local Minima : Points at which the left and right neighbours have more function value are called local minima.

Pls hurry! 15 pts! consider the function f(x)=x^3+2x^2-3. (a) graph the function. (b) what are the

Answer from: Quest

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Answer from: Quest

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Pls hurry! 15 pts!

consider the function f(x)=x^3+2x^2-3. (a) graph the function. (b) w...

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