SOLUTION: If x is 2,3,4 and Y is 11,49,123 what is the rule? I have tried everything and am stumped. I do believe that exponents is the way to answer this equation, but still can not fi

Algebra ->  Matrices-and-determiminant -> SOLUTION: If x is 2,3,4 and Y is 11,49,123 what is the rule? I have tried everything and am stumped. I do believe that exponents is the way to answer this equation, but still can not fi      Log On


   

Question 391708: If x is 2,3,4 and Y is 11,49,123 what is the rule?
I have tried everything and am stumped. I do believe that exponents is the way to answer this equation, but still can not figure it out. Please Help!?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Try a quadratic equation  y = ax²+ bx + c

Substitute x = 2 and y = 11

  y = ax²+ bx + c
 11 = a(2)²+ b(2) + c
 49 = a(3)²+ b(3) + c
123 = a(4)²+ b(4) + c

Simplify:

 11 =  4a + 2b + c
 49 =  9a + 3b + c
123 = 16a + 4b + c

Solve that system of equations and get

a = 18, b = -52, c = 43

So an equation that fits the given data is:

 y = ax²+ bx + c
 y = 18x²- 52x + 43

Edwin