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
Natasha2012 [34]
2 years ago
10

The function f(x) = x3 – 8x2 + x + 42 has zeros located at 7, –2, 3. Verify the zeros of f(x) and explain how you verified them.

Describe the end behavior of the function.
Mathematics
1 answer:
xeze [42]2 years ago
3 0

Answer:

  • zeros are {-2, 3, 7} as verified by graphing
  • end behavior: f(x) tends toward infinity with the same sign as x

Step-by-step explanation:

A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.

<h3>Zeros</h3>

The attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.

<h3>End behavior</h3>

The leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.

  • x → -∞; f(x) → -∞
  • x → ∞; f(x) → ∞

__

<em>Additional comment</em>

The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.

We know the x^2 coefficient is the opposite of the sum of the zeros:

  -(7 +(-2) +3) = -8 . . . . x^2 coefficient

And we know the constant is the opposite of the product of the zeros:

  -(7)(-2)(3) = 42 . . . . . constant

These checks lend further confidence that the zeros are those given.

(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)

You might be interested in
PLSSS HELP ASAPPP I'LL GIVE YOU BRAINLIEST IF I GET IT RIGHT!!!​
kondor19780726 [428]

Answer:

D. 76

Step-by-step explanation:

because students that has 5 absences and less most likely to get higher than 75 marks. The student who has 8 absences studied at home, he's a genius

3 0
2 years ago
HELP ME PLZZZ!!! Solve for x. Show each step of the solution. 4.5(4 − x) + 36 = 202 − 2.5(3 + 28)
Veronika [31]
4.5{4_x}+36=202-2.5{3+28}
you first multiply 4.5 and the numbers in the bracket.
4.5*4=18
4.5*x=4.5x
you will obtain 18-4.5x=202_2.5{3+28}
2.5*3=7.5 2.5*28=70
18_4.5x=202_7.5_70
18_4.5x=124.5_18
-4.5x=106.5
x=23.67
5 0
2 years ago
Write an equation <br><br> 1) y=3<br> 2) y=3/4+3<br> 3) y=3/4x+3<br> 4) y=4
lianna [129]

Answer:

It B

Step-by-step explanation:

This is because the y-intercept is 3 and it going down

Hope this Helped

8 0
2 years ago
Read 2 more answers
4. Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix.
valentina_108 [34]

Answer:

vertex - (0,0)

focus - (0, 3/4)

directrix - 3/4

parabola- x^2=-3y

graph of equation:

8 0
2 years ago
Find the product
o-na [289]

Answer:

2x^3 - 2x^2  - 12x

Step-by-step explanation:

2x(x - 3)(x + 2)

= 2x ( x^2 + 2x -3x - 6)

= 2x (x^2 - x - 6)

= 2x^3 - 2x^2  - 12x (answer).

7 0
2 years ago
Read 2 more answers
Other questions:
  • How much did Briana save by purchasing a backpack that costs $45 with a sales promotion of 20% off instead of a backpack that co
    15·2 answers
  • My office is 11 feet wide and 13 feet long with the ceiling being 8 feet above the floor. I would like to paint the walls light
    7·1 answer
  • Need help ASAP please
    7·2 answers
  • The ratio of men to women working for a company is 8 to 5 . If there are 125 women working for the company, what is the total nu
    14·2 answers
  • Last year 40 people adopted a mantee through Fia's foundation. This year 30% more people adopted a manatee . How many people ado
    8·2 answers
  • ∆ABC, &lt;B=90 •<br>|AC|=50cm |BCI=14cm Find AB.​
    5·1 answer
  • What are the coordinates closest to the park?
    9·2 answers
  • Which would be on the x and y axis of a graph
    15·1 answer
  • Two ferries start moving toward each other from opposite riverbanks, a and b. when they pass each other for the first time, the
    6·2 answers
  • Translate the sentence into an inequality.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!