parabola

If the line of symmetry  is  x =2.....then this is the x coordinate of the  vertex

We have the form

y =  a(x - h)^2  + k         where  h  is the  x oordinate of the vertex ....we need to find a  and k thusly

1  = a  (1 - 2)^2  +  k   →  1  = a  +  k

-1  = a  (5 - 2)^2  + k  → -1  = 9a + k

Subtract  the second equation from the first

2  = -8a

a = 2/-8  = -1/4

And   1 =  -1/4  +  k

k  = 1 + 1/4  = 5/4

So  we  have that

y  =(-1/4) ( x - 2)^2 +  5/4

y = (-1/4)  ( x^2  -4x  + 4) + 5/4

y = (-1/4)x^2  + x  -1  +  5/4

y  = (-1/4)x^2  + x  + 1/4

a = -1/4    b  =  1     c   =   1/4

And their sum is     1