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Elenna [48]
2 years 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]2 years 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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Give the slope and the y-intercept of the line y = x – 4.
Airida [17]

Given:

The equation of a line is

y=x-4

To find:

The slope and y-intercept of the line.

Solution:

We have,

y=x-4          ...(i)

The slope intercept form of a line is

y=mx+b            ...(ii)

Where, m is the slope and b is the y-intercept.

On comparing (i) and (ii), we get

m=1,b=-4

Slope of the line = 1

y-intercept of the line = -4

The coordinate form of y-intercept is (0,b). So, the y-intercept of the given line is (0,-4).

Therefore, the slope of the line is 1 and the y-intercept is (0,-4).

5 0
3 years ago
Dave collects rocks. he makes 12 groups of 10 rocks and has none left over. How many rocks does Dave have?
Firdavs [7]
That means he has 120 rocks
12*10=120

4 0
4 years ago
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Find the missing angle on the triangle pls need help
Maslowich
Answer:
Angle B is 44 degrees.
This is a right triangle.

Steps:
The sum of interior angles in a triangle equals 180 degrees. The given triangle is a right triangle.

So A + B + C = 180
We are given A and C.
46 + B + 90 = 180
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4 0
1 year ago
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Can someone help me plz​
alexandr1967 [171]

Answer:

B. & E.

Step-by-step explanation:

First, to find your slope, put your line into slope-intercept form.

y=mx+b\\

3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4} x-\frac{7}{4}

Your slope is \frac{3}{4}.

Now, you can find the y-intercept of your parallel line by plugging your given point and your slope into point-slope form.

y-y1=m(x-x1)\\y-(-2)=\frac{3}{4} (x-(-4))\\y+2=\frac{3}{4} (x+4)\\y+2=\frac{3}{4} x+3\\y=\frac{3}{4} x+1

Your y-intercept is 1.

If you notice, answer choice E is equivalent to one of our steps in converting it to point-slope form. Therefore, E is one of your answers.

The equation of your parallel line is:

y=\frac{3}{4} x+1

B is also a correct answer.

If you put B into slope-intercept form, you get the following:

3x-4y=-4\\-4y=-3x-4\\y=\frac{3}{4} x+1

This, of course, is equivalent to the parallel line which we already found, so we know it is parallel.

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4 years ago
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Which set of statements shows the correct steps to find 45% of 75
madreJ [45]

Answer:

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Step-by-step explanation:

How much is 45 out of 75 written as a percentage? Convert fraction (ratio) 45 / 75 Answer: 60%

(happy to help)

8 0
4 years ago
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