math

posted by .

The following set of points belong to a specific function:
{(-3,0)(-2,4), (-1,0), (0,-6),(1,-8), (2,0),(3,24)}
Based on the set of points answer the following questions:

b) Write an equation

• math -

Through n +1 points passing polynomial of degree n.

In this case you have 7 points.

Polynomial will be degree 6.

Write the polynomial in this form :

a * x ^ 6 + b * x ^ 5 + c * x ^ 4 + d * x ^ 3 + e * x ^ 2 + f *x + g = y

Now put values of x an y in this equation.

a * ( - 3 ) ^ 6 + b * ( - 3 ) ^ 5 + c * ( - 3 ) ^ 4 + d * ( - 3 ) ^ 3 + e * ( - 3 ) ^ 2 + f * ( - 3 ) + g = 0

a * ( - 2 ) ^ 6 + b * ( - 2 ) ^ 5 + c * ( - 2 ) ^ 4 + d * ( - 2 ) ^ 3 + e * ( - 2 ) ^ 2 + f * ( - 2 ) + g = 4

a * ( - 1 ) ^ 6 + b * ( - 1 ) ^ 5 + c * ( - 1 ) ^ 4 + d * ( - 1 ) ^ 3 + e * ( - 1 ) ^ 2 + f * ( - 1 ) + g = 0

a * 0 ^ 6 + b * 0 ^ 5 + c * 0 ^ 4 + d * 0 ^ 3 + e * 0 ^ 2 + f * 0 + g = - 6

a * 1 ^ 6 + b * 1 ^ 5 + c * 1 ^ 4 + d * 1 ^ 3 + e * 1 ^ 2 + f * 1 + g = - 8

a * 1 ^ 6 + b * 1 ^ 5 + c * 1 ^ 4 + d * 1 ^ 3 + e * 1 ^ 2 + f * 1 + g = - 8

a * 2 ^ 6 + b * 2 ^ 5 + c * 2 ^ 4 + d * 2 ^ 3 + e * 2 ^ 2 + f * 2 + g = 0

a * 3 ^ 6 + b * 3 ^ 5 + c * 3 ^ 4 + d * 3 ^ 3 + e * 3 ^ 2 + f * 3 + g = 24

OR

729 a - 243 b + 81 c - 27 d + 9 e - 3 f + g = 0

64 a - 32 b + 16 c - 8 d + 4 e - 2 f + g = 4

a - b + c - d + e - f + g = 0

0 + 0 + 0 + 0 + 0 + 0 + g = - 6

a + b + c + d + e + f + g = - 8

64 a + 32 b + 16 c + 8 d + 4 e + 2 f + g = 0

729 a + 243 b + 81 c + 27 d + 9 e + 3 f + g = 24

Solutions of this system of equations are :

a = 0

b = 0

c = 0

d = 1

e = 2

f = - 5

g = - 6

y = 0 * x ^ 6 + 0 * x ^ 5 + 0 * x ^ 4 + 1 * x ^ 3 + 2 * x ^ 2 + ( - 5 ) * x + ( - 6 )

y = x ^ 3 + 2 x ^ 2 - 5 x - 6

That is cubic parabola.

• math -

If you want to see graph go on :

wolframalpha dot com

When page be open in rectangle type :

intepolating polynomial {(-3,0),(-2,4), (-1,0), (0,-6),(1,-8), (2,0),(3,24)}

and click option =

You will see graph

Similar Questions

1. math-calc

Consider the function f(x)= (2x+8)/(6x+3). For this function there are two important intervals: (-inf, A) (A, inf) and where the function is not defined at A . Find A For each of the following intervals, tell whether is increasing …
2. calc

Let f be the function defined by f(x) = (x 2 + 1)e -x for -4 < x < 4. a. For what value of x does f reach its absolute maximum?
3. statistics

Job Sat. INTR. EXTR. Benefits 5.2 5.5 6.8 1.4 5.1 5.5 5.5 5.4 5.8 5.2 4.6 6.2 5.5 5.3 5.7 2.3 3.2 4.7 5.6 4.5 5.2 5.5 5.5 5.4 5.1 5.2 4.6 6.2 5.8 5.3 5.7 2.3 5.3 4.7 5.6 4.5 5.9 5.4 5.6 5.4 3.7 6.2 5.5 6.2 5.5 5.2 4.6 6.2 5.8 5.3 5.7 …
4. math

4. For Questions 4-7, use the following data: The number of file conversions performed by a processor per day for 10 days was: 15, 27, 25, 28, 30, 31, 22, 25, 27, 29 What is the arithmetic mean of the data?
5. Math

Question 2 For the function f(x) = 3x2-2x-7, find f(2). Answer f(2) = 13 f(2) = 25 f(2) = 1 f(2) = 1/2 3 points Question 3 One day you work 3 hours and your boss gives you \$22. Another day after working 4 hours your boss gives you …

Did I get these practice questions right?
7. Calculus

Answer the following questions for the function f(x)=(x^3-9x^2+27x-27)/(x^2-6x+8) defined on the interval [-14, 22]. Enter points, such as inflection points in ascending order. A. The function f(x) has vertical asymptotes at _______ …
8. math

Part A: Does the table represent a relation that is a function?
9. Algebra 2

Evaluate the function when x=1. f(x)=4x-2. Write the input and output as a set of ordered pairs, and identify the domain and range of the ordered pair. (6 points) Ordered Pair: Domain: Range: Write an equation of direct variation that …
10. Calc

Find the set of points that the following function is continuous at them. f(x)= { √(5-x) -2 if x < 1 , (2x-1 + In(x)) / (x-25) if x>1, -1/24 if x=0

More Similar Questions