Use quadratic regression to find a function that fits the following points. (-2,-16), (3,11), (0,2).

  y = -1.2x² +6.6x +2

Step-by-step explanation:

The quadratic regression function of a calculator or spreadsheet can do this for you. The resulting function is ...

  y = -1.2x² +6.6x +2

_____

If you want to do this by hand, put the given (x, y) values into the formula ...

  ax² +bx +c = y

and solve the resulting system of equations.

The third point tells you c=2, so you can simplify the system of equations to ...

  a(-2)² +b(-2) +2 = -16   ⇒   4a -2b = -18   ⇒   2a -b = -9

  a(3)² +b(3) +2 = 11   ⇒   9a +3b = 9   ⇒   3a +b = 3

Adding these equations together gives ...

  (2a -b) +(3a +b) = (-9) +(3)

  5a = -6 . . . . . . . . simplify

  a = -1.2 . . . . . . . divide by 5

  b = 3 -3a = 3 -3(-1.2) = 6.6 . . . . from the second equation

Now we know the coefficients are a=-1.2, b=6.6, c=2, so the function is ...

  y = -1.2x² +6.6x +2

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step-by-step explanation: