A parabola with equation y = x^2 + bx + c passes through the points (2,3) and (4,3). What is c?
Instead of knowing the constants and solving for a point, we are given two points and asked to solve for the constants.
First plug in the two points to the equation.
(2,3)=(x,y) plugged into y=x^2+bx+c
subtract 4 from each side
subtract 16 from each side
Now this problem is only a matter of solving a system of equations:
Subtract the second one from the first one to eliminate c:
divide by 2
Substitute -6 in for b to get c:
add 12 to each side