\(\text{A parabola with equation $y=x^2+bx+c$ passes through the points $(2,3)$ and $(4,3)$. What is $c$? }\)
\(\text{just plug the points in and solve the resulting equations}\\ 2^2 + b(2) + c = 3\\ 4^2 + b(4) + c = 3\\~\\ 4 + 2b + c = 3\\ 16+4b+c = 3\\ \text{subtract twice (1) from (2)}\\ 8-c=-3\\ c=11\)
