y[x_, c_] := -x^2 + c

Manipulate[
    Grid[{
       { ymax = FindMaximum[{y[x, c], -1 <= x <= 1}, x] },
       { Plot[y[x, c], {x, -1, 1}] }
    }],
{c, -0.5, 0.5}]

In[3]:= ymax
Out[3]:= {-0.5, {x -> -1.70726*10^-14}}

In[4]:= ymax = FindMaximum[{y[x, 2], -1 <= x <= 1}, x]
Out[4]:= {2, {x -> -1.70726*10^-14}}

In[5]:= ymax
Out[5]:= {-0.5, {x -> -1.70726*10^-14}}

ClearAll["Global`*"]

y[x_, c_] := -x^2 + c

Manipulate[
 Print["enter"];
 Grid[{
   {ymax = FindMaximum[{y[x, c], -1 <= x <= 1}, x]},
   {Plot[y[x, c], {x, -1, 1}]}}
  ],
 {c, -0.5, 0.5},
 TrackedSymbols :> {c}
 ]