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!

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

To Calculate Some Important Points :

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).

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 is not a root.

Now, let x=1

∴ 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

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.

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24