Find the quadratic function that is the best fit for f(x) defined by the table below

Y = ax² + bx + c 
We have to calculate a, b and c from the given table

1st Calculate c:
for x = o, y = -1.55 
- 1.55 = a(0)² + b(0) + c → then c = -1.55
and the equation becomes: y = ax² + b.x - 1.55

2nd Calculate a and b:
for x = 2 , y = 17.29
17.29 =a(2)² + b(2) - 1.55 → 4a + 2b - 1.55 = 17.29 or 4a + 2b = 18.84 (1)

for x = 4 , y = 54.93
54.93=a(4)² + b(4) - 1.55 → 16a + 4b - 1.55 = 54.93 or 16a + 4b = 56.48 (2)

Now solve the system of 2 equations:
4a + 2b = 18.84 (1)
16a + 4b = 56.48 (2)

And you will find :

a= 2.35   and b = 4.72 . And the final equation is:

y = 2.35.x² + 4.72x - 1.55