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
seraphim [82]
3 years ago
5

Please help me answer this question. Show steps and explain

Mathematics
1 answer:
salantis [7]3 years ago
3 0

Your problem statement makes no reference to p or q, so we can only guess that "p/q" refers to the ratio of the lowest- and highest-degree coefficients:

... -6/1

Then the factors of p/q are the factors of 6, with either sign.

Factors of p/q: ±1, ±2, ±3.

There are a number of ways the factors can be tested. To test 1, simply add the coefficients. (The sum is -8.) To test -1, subtract the sum of odd-degree coefficients from the sum of even-degree coefficients. (The difference is 0.)

Knowing that -1 is a root of the function, you can use synthetic division to find the quadratic factor. (See the first attachment for the work.) Then you have ...

... f(x) = (x +1)(x² +x -6)

You can continue to test the factors of p/q, or you can factor the quadratic to get ...

... f(x) = (x +1)(x -2)(x +3)

Another way to test the factors is to program your graphing calculator to evaluate the function f(x) for those factors. The result from my TI-84 is shown in the second attachment. That shows f(x) = 0 for x = -3, -1, and +2.

Test the factors: f({-3, -2, -1, 1, 2, 3}) = {0, 4, 0, -8, 0, 24}

This tells you the x-intercepts.

X-intercepts: -3, -1, 2

Of course, the y-intercept is just the constant in the function—the value of the function when x=0.

Y-intercept: -6

As with any odd-degree polynomial with a positive leading coefficient, the overall behavior looks like "/". That is ...

End behaviors: f(x) goes to -∞ as x goes to -∞; f(x) goes to +∞ as x goes to +∞.

_____

A graph of f(x) is shown in the third attachment. (Graphing calculators make it easy to use graphing to find x-intercepts.)

You might be interested in
Tonya is twice Kevin's age. In three years, Tonya will be 17. And in another three years, Uncle Rob will be three times Tonya’s
kozerog [31]
Kevin is 7. Uncle rob is 60.
6 0
3 years ago
Order of operations problem help! Thank you !
zubka84 [21]
13 hope this helps!!
4 0
3 years ago
Read 2 more answers
Peter paid $12.83 for a DVD. The price of the DVD was $11.99. How much sales tax did Peter pay?
Bas_tet [7]
<span>Peter paid </span>84 cent in taxs
8 0
3 years ago
Read 2 more answers
PLEASE ANSWER:Which of the following are examples of exponential growth? Select all that apply Shasta increases the amount she s
Monica [59]
Answers: Shasta increases the amount she saves each month by 5%. The amount of cell phone subscribers in a small town increases by 75% each year.The price of a stock goes up 12% each year. 
Exponential growth consistently raises the base amount/number to a certain degree. The above answers increase a digit by a number of percentage steadily over a period of time. 
4 0
3 years ago
Read 2 more answers
Sally has to pay a deposit to rent a kayak of $50.00, then she is charged $7.00 per hour
solmaris [256]

Answer:

$92

Step-by-step explanation:

Since Sally plans to keep the kayak for 6 hours and it's $7 per hour we can multiply 6*7 to determine how much she will be charged for keeping the kayak.

6*7=$42

Now we add this to the original deposit of $50.

$50+$42=$92

4 0
2 years ago
Other questions:
  • A card is drawn from a standard deck of playing cards. what is the probability that the card is either a 9 or a 10? (express you
    13·1 answer
  • The variable Z is directly proportional to X. When X is 3, Z has the value 57. What is the value of Z when X = 8
    12·1 answer
  • What is the solution
    13·1 answer
  • What is the value of x?<br>(3x - 14)<br>X<br>[4(X-9)<br>Enter your answer in the box.<br>​
    9·1 answer
  • What is the circumference of a 18in circle
    7·1 answer
  • Find the value of x if h(x) = -25 in the function h(X) = 1/5x + 10
    15·2 answers
  • Solve the inequality <br><br>2r^2-13x+15&lt;0​
    8·2 answers
  • This diagram is not drawn to scale. Based on the information in the diagram, which of the following statements are true? Select
    7·1 answer
  • Write all perfect squares between 26 and 125​
    15·1 answer
  • Geometry help please. Thank you. I picked C but that answer is wrong. What term Describes RT?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!