$\begin{array}{l}y=a x^{2}+b x+c \\ 2=a(0)^{2}+b(0)+c\end{array}$
\(\boxed{c = 2}\)
Step 1 :Given the quadratic equation: \(y = ax^2 + bx + c\) and the point \((0, 2)\) on the curve.
Step 2 :Plug in the x and y values from the point into the equation: \(2 = a(0)^2 + b(0) + c\)
Step 3 :Simplify the equation: \(2 = 0 + 0 + c\)
Step 4 :Find the value of c: \(c = 2\)
Step 5 :\(\boxed{c = 2}\)