SOLUTION: Write an equation to represent each relation, {(-6,4),(-3,8),(1,-24),(2,-12),(6,-4)} and {(-4,3),(-2,12),(-1,48),(1,48),(2,12)}

Algebra ->  Functions -> SOLUTION: Write an equation to represent each relation, {(-6,4),(-3,8),(1,-24),(2,-12),(6,-4)} and {(-4,3),(-2,12),(-1,48),(1,48),(2,12)}      Log On


   

Question 407012: Write an equation to represent each relation, {(-6,4),(-3,8),(1,-24),(2,-12),(6,-4)} and {(-4,3),(-2,12),(-1,48),(1,48),(2,12)}
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!

{(-6,4),(-3,8),(1,-24),(2,-12),(6,-4)} 

Assume a polynomial equation of one less degree than the number 
of points given.  There are 5 points given, so we assume a 4th 
degree equation:

y+=+Ax%5E4+%2B+Bx%5E3+%2B+Cx%5E2+%2B+Dx+%2B+E

Substituting each of the five given points into that equation:

4+=+A%28-6%29%5E4+%2B+B%28-6%29%5E3+%2B+C%28-6%29%5E2+%2B+D%28-6%29+%2B+E
8+=+A%28-3%29%5E4+%2B+B%28-3%29%5E3+%2B+C%28-3%29%5E2+%2B+D%28-3%29+%2B+E
-24+=+A%281%29%5E4+%2B+B%281%29%5E3+%2B+C%281%29%5E2+%2B+D%281%29+%2B+E
-12+=+A%282%29%5E4+%2B+B%282%29%5E3+%2B+C%282%29%5E2+%2B+D%282%29+%2B+E%29+
-4+=+A%286%29%5E4+%2B+B%286%29%5E3+%2B+C%286%29%5E2+%2B+D%286%29+%2B+E+

That becomes the system:

        

Solve that system of equations and get

A=-1%2F9, B=0, C=43%2F9, D=-2%2F3, E=-28

So the equation 

y+=+Ax%5E4+%2B+Bx%5E3+%2B+Cx%5E2+%2B+Dx+%2B+E+

becomes

y+=+expr%28-1%2F9%29x%5E4+%2B+expr%2843%2F9%29x%5E2+-+expr%282%2F3%29x+-28

and the graph of it is:



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Your second problem is done the same way.  The answer is

y+=+expr%283%2F4%29x%5E4+-+expr%2863%2F4%29x%5E2+%2B63

Edwin