math
posted by FUNCTIONS .
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

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. 
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
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