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
Elenna [48]
1 year ago
13

The graph of a quartic function crosses the x-axis at -4 and -2 and touches it at 3. State the equation for the family.

Mathematics
1 answer:
nekit [7.7K]1 year ago
6 0

The equation of the <em>quartic</em> function is f(x) = x⁴ - 18 · x² + 6 · x + 72.

<h3>How to find the possible equations for a quartic polynomial that passes through the x-axis at three points</h3>

Herein we must construct at least a polynomial that satisfies all conditions described in the statement. According to the fundamental theorem of algebra, <em>quartic</em> functions may have no <em>real</em> roots, two <em>real</em> roots or four <em>real</em> roots, which means that one of the roots must have a multiplicity of 2.

The root with a multiplicity of 2 is x = 3 and both x = - 4 and x = - 2 have only a multiplicity of 1, then we have the following expression by using the <em>factor</em> form of the definition of polynomials:

f(x) = (x - 3)² · (x + 4) · (x + 2)

Now we expand the expression to get the <em>standard</em> form:

f(x) = (x² - 6 · x + 9) · (x² + 6 · x + 8)

f(x) = x⁴ - 6 · x³ + 9 · x² + 6 · x³ - 36 · x² + 54 · x + 8 · x² - 48 · x + 72

f(x) = x⁴ - 18 · x² + 6 · x + 72

To learn more on quartic functions: brainly.com/question/25285042

#SPJ1

You might be interested in
2÷9<br><img src="https://tex.z-dn.net/?f=78%20%5Csqrt%7B%7D%20" id="TexFormula1" title="78 \sqrt{} " alt="78 \sqrt{} " align="ab
dimulka [17.4K]

Answer:

2 ÷ 9 ≈ 0.222

√78 ≈ 8.832

3 0
3 years ago
Can someone help me with this question????PLEASE
kiruha [24]
Divide the number of quarts of beef soup by the number of cups of vegetables.
1000 / 510

you should get 1.96
If your teacher wants you to round up you should try 2.
3 0
3 years ago
Read 2 more answers
A company manufactures 295 toy car each day. How many toy cars dose the company manufacture in 34 days?
exis [7]

295 X 34 = 10030 <== Cars in 34 days

3 0
3 years ago
Read 2 more answers
A plane perpendicular to the base of a cone passes through the apex. Which shape is formed by the intersection?
worty [1.4K]

Answer:

  D) triangle

Step-by-step explanation:

The attached image may be helpful to visualizing what the cross section looks like. It is a triangle.

5 0
3 years ago
Read 2 more answers
Probability.....................................
lisabon 2012 [21]

Answer:

1) Mutually exclusive

2) Overlapping or inclusive

3 0
3 years ago
Other questions:
  • A store is having a 25•/• off sale on all shirts. show two ways to calculate the sale price for a shirt that normally costs $24.
    8·2 answers
  • What is the factorization of the trinomial below? 14x^2-39x-35
    13·1 answer
  • Suppose f(x)=x^2 and g(x)=(1/3X)^2. Which statement best compares the graph of g(x) with the graph of f(x)?
    10·2 answers
  • What the slope and y intercept ? and how did you find it ?
    14·1 answer
  • The Emerson First National Bank is lending you money to buy a new car. The loan agreement will probably state that you must carr
    9·2 answers
  • What times itself equal 53.38
    8·1 answer
  • 1. 4x8/12=m <br><br> what is m
    12·1 answer
  • Help me please I don’t have a lot of time please.
    7·1 answer
  • The cost of a movie ticket depends on your age . the piecewise function below gives the cost of a movie ticket for children , ad
    14·1 answer
  • The probability of picking a quarter from a jar of coins is 0.125. If Cindy has 280 coins in the jar, how many quarters are in t
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!