SOLUTION: I'm working on function tables right now and the x values are 12,24, 26, and the y values are 5, 10, 15. I'm having trouble finding the equation for the table. Can you help me?

Algebra ->  Functions -> SOLUTION: I'm working on function tables right now and the x values are 12,24, 26, and the y values are 5, 10, 15. I'm having trouble finding the equation for the table. Can you help me?       Log On


   



Question 1149957: I'm working on function tables right now and the x values are 12,24, 26, and the
y values are 5, 10, 15. I'm having trouble finding the equation for the table.
Can you help me?

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
x | 12 | 24 | 26 |
y |  5 | 10 | 15 |

We can assume it is of this form, 
a quadratic function: 

f(x) = Ax² + Bx + C

f(12) = A(12)² + B(12) + C = 5
      =   144A +   12B + C = 5

f(24) = A(24)² + B(24) + C = 10
      =   576A +   24B + C = 10

f(26) = A(26)² + B(26) + C = 15
      =   676A +   26B + C = 15

So we have the system of equations:

system%28144A%2B12B%2BC=5%2C576A%2B24B%2BC=10%2C%0D%0A676A%2B26B%2BC=15%29

Solving that system gives



So one function that fits the data of the table is:

%22f%28x%29%22=expr%2825%2F168%29x%5E2-expr%28-415%2F84%29x%2B300%2F7%29

Edwin