A parabola with equation y=x^2+bx+c passes through the points (2,3) and (4,3). What is c?
We have these two equations
3 = (2)^2 + 2b + c
3 = (4)^2 + 4b + c simplify
3 = 4 + 2b + c
3 = 16 + 4b + c
-1 = 2b + c ⇒ 2 = -4b - 2c (1)
-13 = 4b + c (2)
Add (1) and (2) and we have
-11 = -c
c = 11
