Posted by **FUNCTIONS** on Friday, July 5, 2013 at 10:19pm.

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:

a) What type of function does it produce? Justify your answer.

b) Write an equation

- math -
**Bosnian**, Saturday, July 6, 2013 at 3:27am
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

Your Polynomial :

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 -
**Bosnian**, Saturday, July 6, 2013 at 6:50am
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

## Answer this Question

## Related Questions

- math - 4. For Questions 4-7, use the following data: The number of file ...
- math-calc - Consider the function f(x)= (2x+8)/(6x+3). For this function there ...
- Calculus, check my answers, please! 3 - Did I get these practice questions right...
- Calculus - Answer the following questions for the function f(x)=(x^3-9x^2+27x-27...
- 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...
- Math - Question 2 For the function f(x) = 3x2-2x-7, find f(2). Answer f(2) = 13 ...
- Math - The graph of the equation y=4-x consists of all the points in the ...
- Reiny!!!! math help - We understand how to do the questions now and we are ...
- calculus - suppose the set of points have the following coordinates:(-2,3),(4,-4...
- Algebra - 84. Examine the following set of coordinates. Does this set come from ...