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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

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From 9pm to 6am the tempeture dropped 1.6 degrees Fahrenheit per hour what was the total change in temperature in degrees Fahren
aalyn [17]
1.6 (degrees) x 9 (hours) = 14.4 degrees
4 0
2 years ago
If it took Carlos 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 mile
Dvinal [7]

Answer:

Step-by-step explanation:

Given

time taken by Carlos to cycle is t=0.5\ hr

For case (1)

Average speed v_{avg}>16\ ft/s

For 0.5 hr \approx 30\times 60=1800\ s

Distance traveled d=1800\times 16=28,800\ ft\approx 5.45\ miles

Therefore Carlos might not be able to cover 6 miles with average speed of  16 ft/s

(2)v_{avg}=18\ ft/s

for 0.5 hr

distance traveled

d=1800\times 18=32,400\ ft\approx 6.136

Therefore Carlos might be able to cover more than 6 miles with 18\ ft/s

5 0
3 years ago
Please can someone help me with this​
kobusy [5.1K]

Answer:

1 : 0.44.

Step-by-step explanation:

93 : 41

= (93/93) : (41/93)

= 1 : 0.44.

6 0
2 years ago
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
skad [1K]

Answer:

Follow the steps and it will help on all the problems and it should help you out.

Step-by-step explanation:

  1. You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.
  2. You only multiply or divide, never add or subtract, to get an equivalent fraction.
  3. Only divide when the top and bottom stay as whole numbers.

8 0
3 years ago
Read 2 more answers
Separate the number 219 into three parts. The second number is two less than 5 times the first number, and the third number is 4
Sav [38]
Let us assume the first number = x
Then the second number = 5x -2
The third number = x + 4
The total number that needs to be divided into three parts is 219
Then we can write the equation as
x + 5x - 2 + x + 4 = 219
7x + 2 = 219
7x = 219 - 2
7x = 217
x = 217/7
  = 31
Then
First number = 31
Second number = 5x - 2
                           = (5 * 31) - 2
                           = 155 -2
                          = 153
Third number = x + 4
                       = 31 + 4
                       = 35
So the three numbers are 31, 153 and 35.
4 0
3 years ago
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