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
AnnyKZ [126]
2 years ago
12

What key features are necessary and how they can be used to create the sketch of a polynomial function?

Mathematics
1 answer:
Tomtit [17]2 years ago
4 0

The key features of polynomials are the vertex, axis of symmetry, x and y intercepts.

 

<span>1.    </span>The degree will help you find the end behavior.

<span>2.     </span>The vertex shows you where it changes concavity.

<span>3.     </span>X and y intercepts give you a couple of points of reference.

<span>4.     </span>Axis of symmetry is only applicable to even degree polynomials.

 

I am hoping that these answers have satisfied your queries and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

You might be interested in
Circle the value that solutions of the inequality 2x - 3 &lt; -9
velikii [3]

Answer:

x < -3

Step-by-step explanation:

2x - 3 < -9

Add 3 to each side

2x - 3+3 < -9+3

2x < -6

Divide by 2

2x/2 < -6/2

x < -3

5 0
2 years ago
What is the area of the shape given above?!? Someone please help this is due today
LenaWriter [7]

Answer:

15 m

Step-by-step explanation:

First split the shape into a square and a triangle, then find the area of the square by multipliyng the sides to get.

Next find the length of the traignel by subtracting 3 from 9 to get for then find the area of the triangle by multiplying 4 by 3 to get 12 then divide by 2 to get the area which is 6.  

Finally add the 9 to the 6 to get 15

3 * 3 = 9

9 - 3 = 4

4 * 3 = 12/2 = 6

6+9=15

7 0
2 years ago
A student bought 34 pencils for school.if he sharpened 16 of the pencils before school whats is his ratio of unsharpened pencils
Sergio [31]


he bought 34 pencils which I suppose aren't already sharpened

so if he sharpens 16 of them just subtract 16 from 34 (34-16) which equals 18

so the ratio would be 16:18

but if u need to simplify it would be 8:9

3 0
2 years ago
New friends?<br> whats 1+1?
wel

Answer:

2

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
(a) Determine a cubic polynomial with integer coefficients which has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.
Keith_Richards [23]

Answer:

(a) x\³ - 6x - 6

(b) Proved

Step-by-step explanation:

Given

r = $\sqrt[3]{2} + \sqrt[3]{4}$ --- the root

Solving (a): The polynomial

A cubic function is represented as:

f = (a + b)^3

Expand

f = a^3 + 3a^2b + 3ab^2 + b^3

Rewrite as:

f = a^3 + 3ab(a + b) + b^3

The root is represented as:

r=a+b

By comparison:

a = $\sqrt[3]{2}

b = \sqrt[3]{4}$

So, we have:

f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3

Expand

f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4

f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4

f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4

f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4

Evaluate like terms

f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)

Recall that: r = $\sqrt[3]{2} + \sqrt[3]{4}$

So, we have:

f = 6 + 6r

Equate to 0

f - 6 - 6r = 0

Rewrite as:

f - 6r - 6 = 0

Express as a cubic function

x^3 - 6x - 6 = 0

Hence, the cubic polynomial is:

f(x) = x^3 - 6x - 6

Solving (b): Prove that r is irrational

The constant term of x^3 - 6x - 6 = 0 is -6

The divisors of -6 are: -6,-3,-2,-1,1,2,3,6

Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values

f(-6) = (-6)^3 - 6*-6 - 6 = -186

f(-3) = (-3)^3 - 6*-3 - 6 = -15

f(-2) = (-2)^3 - 6*-2 - 6 = -2

f(-1) = (-1)^3 - 6*-1 - 6 = -1

f(1) = (1)^3 - 6*1 - 6 = -11

f(2) = (2)^3 - 6*2 - 6 = -10

f(3) = (3)^3 - 6*3 - 6 = 3

f(6) = (6)^3 - 6*6 - 6 = 174

For r to be rational;

The divisors of -6 must divide f(x) without remainder

i.e. Any of the above values  must equal 0

<em>Since none equals 0, then r is irrational</em>

3 0
2 years ago
Other questions:
  • What is 134,500 rounded to the nearest ten thousand
    15·1 answer
  • Joe and Kim washed 27 cars in 6 hours. The next day, they had more help and washed twice as many cars in the same amount of time
    5·1 answer
  • Shyla had a balance of −$255.25 in her account, and Susan had a balance of −$178.75 in her account.
    5·2 answers
  • Help please im confused
    13·1 answer
  • Neal used magnetic letters to spell the word communication on his file cabinet. One of the magnets fell on the floor. What is th
    14·2 answers
  • An executive invests $22,000 some at 7% ad some at 6% annual interest. If he receives an annual return of $1,420, how much is in
    5·1 answer
  • What is the slope of the line wit the points (1,1) and (-2,2)
    9·2 answers
  • Find the mass of the triangle with vertices (1; 0; 0), (0; 2; 0), (0; 1; 1) if the density function is given by (x; y; z)
    14·1 answer
  • Lucia surveyed the students in her class and made a dot plot of the results. What question could Lucia have asked?
    6·1 answer
  • Did ancient mathematicians use a ruler to determine the values of sine and cosine in a circle?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!