Writing quadratic functions from tables?

We will have this system of equations

a(2)^2  + b(2)  + c  = 28.4

a(3)^2  + b(3) + c  = 63.9

a(4)^2  + b(4)  + c  = 113.6       simplifying, we have

4a + 2b + c  = 28.4

9a +  3b + c = 63.9

16a  + 4b + c = 113.6

Subtract the first equation from both the second and third equations and we have this :

5a +  b  = 35.5

12a + 2b  = 85.2

Multiply the  first equation by  -2  and add it to the second equation

-10a -2b  = - 71

12a + 2b  = 85.2

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  2a  =  14.2            divide both sides by  2

a  =  7.1

And using 5a + b = 35.5,  we can solve for b as

5 (7.1) + b = 35.5

35.5 + b  =35.5

b = 0

And using  4a + 2b + c  =28.8  to find c

4(7.1) + 2(0) + c  =28.8

28.8  + c  =28.8

c  = 0

So...our function  is

y  = (7.1 )x^2           and  b  and c  = 0