Let me show you how to solve it without using equations.

We have a parabola, and its ordinate y at x= 1 is the same as the ordinate y at x= 3.


It means that the parabola's symmetry axis is  x= 2  half way between  x= 1  and x= 3.


Hence, the parabola has a vertex at x= 10, and the vertex form equation is


    y = a*(x-2)^2 + 10.


where "a" is a coefficient, now unknown.


To find "a", substitute x= 3 into the vertex form equation.


You will get then


    9 = a*(3-2)^2 + 10,   or


    a*1^2 = 9 - 10

       a  = -1.


So, the vertex form equation is


    y = -(x-2)^2 + 10.


Rewrite it in the general form


    y = -(x^2 - 4x + 4) + 10 = -x^2 + 4x + 6.


Thus  a= -1,  b= 4,  c= 6.


                          P L O T


    


              Plot  y =  =