You have to solve 3 equations pretty much simultaneously here using the x and y values in the general form of the quadratic equation 
Start with the first values of x=0 and y=5.1 to solve for c:
so c = 5.1
Next use the second x and y values along with the value of c in the next equation:
gives you
-2.07 = a + b. Solve this for a:
a = -2.07 - b
Finally use the third set of numbers with the c value AND the subbed value for a:
1.17 = 9(-2.07 - b)+ 3b + 5.1 which simplifies to:
1.17 = -18.63 - 9b + 3b + 5.1 which further simplifies to:
14.7 = -6b and b = -2.45
Now you have c and b, let's find a using one of the simplified equations:
-2.07 = a + b
-2.07 = a - 2.45
a = .38
So here's your equation:
Start with the first values of x=0 and y=5.1 to solve for c:
Next use the second x and y values along with the value of c in the next equation:
-2.07 = a + b. Solve this for a:
a = -2.07 - b
Finally use the third set of numbers with the c value AND the subbed value for a:
1.17 = 9(-2.07 - b)+ 3b + 5.1 which simplifies to:
1.17 = -18.63 - 9b + 3b + 5.1 which further simplifies to:
14.7 = -6b and b = -2.45
Now you have c and b, let's find a using one of the simplified equations:
-2.07 = a + b
-2.07 = a - 2.45
a = .38
So here's your equation: