SOLUTION: Describe whether a quadratic model exists for each set of values. If so, write the model. f(-2) = 16, f(0)=0, f(1)=4. How do I work this equation out?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Describe whether a quadratic model exists for each set of values. If so, write the model. f(-2) = 16, f(0)=0, f(1)=4. How do I work this equation out?      Log On


   

Question 708798: Describe whether a quadratic model exists for each set of values. If so, write the model. f(-2) = 16, f(0)=0, f(1)=4. How do I work this equation out?
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Yes. Quadratic model can be used for those values, because those are three data points, and that is the minimum necessary for a quadratic function. Using those dependent and independent pairs, you can make three equations and the unknown variables will be the three coefficients, a, b, and c.
SYSTEM OF EQUATIONS
%28-2%29%5E2%2Aa%2B%28-2%29b%2Bc=16
%280%29%5E2%2Aa%2B%280%29b%2Bc=0
%281%29%5E2%2Aa%2B%281%29b%2Bc=4
Some arithmetic needs to be taken care of before solving the system.