{(-5,124),(4,25),(-3,60)}

The general quadratic equation is

           y = Ax² + Bx + C

Plug in x = -5, y = 124 into

           y = Ax² + Bx + C
         124 = A(-5)² + B(-5) + C
         124 = A(25) - 5B + C
         124 = 25A - 5B + C
25A - 5B + C = 124

Plug in x = 4, y = 25 into

           y = Ax² + Bx + C
          25 = A(4)² + B(4) + C
          25 = A(16) + 4B + C
          25 = 16A + 4B + C
16A + 4B + C = 25

Plug in x = -3, y = 60 into

           y = Ax² + Bx + C
          60 = A(-3)² + B(-3) + C
          60 = A(9) - 3B + C
          60 = 9A - 3B + C
 9A - 3B + C = 60

Now we have this system of 3 equations in 3 unknowns:

25A - 5B + C = 124
16A + 4B + C = 25
 9A - 3B + C = 60

To eliminate C from the 1st 2 equations,
multiply the 2nd eq. by -1
and add to the 1st:


 25A - 5B + C = 124
-16A - 4B - C = -25
-------------------
  9A - 9B     = 99

Divide that through by 9:

     A - B = 11 

16A + 4B + C = 25
 9A - 3B + C = 60

To eliminate C from the 2nd and 3rd
equations, multiply the 3rd eq. by -1
and add to the 2nd:

16A + 4B + C =  25
-9A + 3B - C = -60
------------------
 7A + 7B     = -35

Divide that through by 7

  A + B = -5

Now we have this system,
which we add directly:

  A - B = 11 
  A + B = -5
 -----------
 2A     =  6
      A = 3

Substitute in 

  A + B = -5
  3 + B = -5
      B = -8

Substitute in 

     9A - 3B + C = 60
9(3) - 3(-8) + C = 60
     27 + 24 + C = 60
          51 + C = 60
               C = 9

So
           y = Ax² + Bx + C

becomes

           y = 3x² - 8x + 9

Edwin