1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Free_Kalibri [48]
3 years ago
7

Find all x-intercepts and y-intercepts of the graph of the function . f(x) = - x ^ 3 + x ^ 2 + 12x If there is more than one ans

wer, separate them with commas. Click on "None" if applicable.
Mathematics
1 answer:
ololo11 [35]3 years ago
3 0

Answer:

The y-intercept is (0,0)

The x-intercepts are (-3,0), (0,0), and (4,0)

Step-by-step explanation:

So we have the function:

f(x)=-x^3+x^2+12x

And we want to solve for the x- and y-intercepts.

Y)

To solve for the y-intercept, recall that the y-intercept is when the graph touches the y-axis. At that point, the x values is 0. Thus, to find the x-intercept, substitute 0 for x:

f(x)=-(0)^3+(0)^2+12(0)

Simplify:

f(x)=0

So, the y-intercept is (0,0)

X)

To solve for the x-intercept(s), set the function equal to 0 and solve for x:

0=-x^3+x^2+12x

First, factor out a negative x:

0=-x(x^2-x-12)

Factor within the parentheses:

0=-x(x-4)(x+3)

Zero Product Property:

-x=0\text{ or } x-4=0\text{ or } x+3=0

Divide by -1 on the first one. Add 4 on the second one. And subtract 3 on the right:

x=0\text{ or } x=4\text{ or } x=-3

So, our x-intercepts are:

(-3,0), (0,0), (4,0)

And we're done :)

You might be interested in
Maya has 3 times as many dimes as nickels. She has 4 more quarters than nickels. if she has a total of $9.40, how many of each t
puteri [66]

Answer:  nickels = 14, dimes = 42, quarters = 18

<u>Step-by-step explanation:</u>

Let n represent nickels <em>which has a value of $0.05 </em>

Let d represent dimes <em>which has a value of $0.10</em>

Let q represent quarters <em>which has a value of $0.25</em>

It is given that:

                       n = n

                      d = 3n

                      q = n + 4

and their total value is $9.40    ⇒     n + d + q = $9.40

Use substitution to find the quantity of nickels:

.05(n) + .10(3n) + .25(n + 4) = 9.40

 5n    +  10(3n) +   25(n+4)   = 940           <em>multiplied by 100 </em>

 5n    +   30n   +  25n + 100 = 940          <em>distributed</em>

                            60n + 100 = 940          <em>added like terms</em>

                            60n           = 840          <em>subtracted 100</em>

                                 n           = 14            <em>divided by 60</em>

n = 14

                d = 3n

                   = 3(14)

                   = 42

                                       q = n + 4

                                          = (14) + 4

                                           = 18

4 0
3 years ago
What equation represents a line that passes through (4,1/3) and has a slope of 3/4
AysviL [449]
\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{\frac{1}{3}})&#10;\qquad \qquad \qquad \qquad &#10;% slope  = m&#10;slope =  m\implies \cfrac{3}{4}&#10;\\\\\\&#10;% point-slope intercept&#10;\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-\cfrac{1}{3}=\cfrac{3}{4}(x-4)\implies y-\cfrac{1}{3}=\cfrac{3}{4}x-3&#10;\\\\\\&#10;y=\cfrac{3}{4}x-3+\cfrac{1}{3}\implies y=\cfrac{3}{4}x-\cfrac{8}{3}
4 0
3 years ago
What is the value of c in the equation? 15.3= C/2.1
geniusboy [140]

Answer:

c=32.13

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A small business reported a net loss of $45 in January and a gain of $55 in February. What is the company's net profit?
frozen [14]
Gain - loss = profit
55- 45 = $10 net profit
5 0
3 years ago
Find the solution of the system of equations.<br>6x + 8y = -8<br>x + 4y = 4<br>( , )​
ladessa [460]

Answer:

the solution is (-4, 2)

Step-by-step explanation:

6x + 8y = -8

x + 4y = 4

... can be solved using elimination by addition and subtraction, among other methods.  Multiply the second equation by -2 to obtain

6x + 8y = -8

-2x - 8y = -8

Combining these results in

4x = -16.  Thus, x = -4.

Substituting -4 for x in x + 4y = 4 results in

-4 + 4y = 4, or 4y = 8, or y = 2

Then the solution is (-4, 2)

8 0
3 years ago
Other questions:
  • 5 + 3 + 2 = 151022
    5·1 answer
  • What if you dont have a median in the lower and upper quartile on a number line?
    5·1 answer
  • Find the slope of the line through (-1,1) and (3, -4)
    6·1 answer
  • A line with a slope of -2 passes through the point (4, 7).
    15·2 answers
  • 3(x+5)&lt;=2(3-x)-1 solve the inequality
    8·1 answer
  • Which equation best models the data in the table below?
    6·1 answer
  • The rare tweety-birds are decreasing at a rate proportional to the
    15·1 answer
  • Which set of ordered pairs represents y as a function of x?
    5·1 answer
  • Give the domain and range of the relation. ​{(-3​,6​), ​(-2​1,​), ​(0,-3​), ​(2​,1​), ​(4​,13​)}
    6·1 answer
  • Select the table that represents the ordered pairs that are plotted in the coordinate plane.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!