Final answer:
The parabola passes through the points (2,3) and (4,3). We can use this information to find the values of b and c in the equation y = x² + bx + c.
Step-by-step explanation:
The equation of the given parabola is y = x² + bx + c. We are given that the parabola passes through the points (2,3) and (4,3). Substitute the x and y coordinates of (2,3) into the equation to get 3 = 2² + 2b + c. Substitute the x and y coordinates of (4,3) into the equation to get 3 = 4² + 4b + c.
Now we have two equations: 2² + 2b + c = 3 and 4² + 4b + c = 3. Subtract the first equation from the second to eliminate c and solve for b. This gives us: (4² + 4b + c) - (2² + 2b + c) = 3 - 3. Simplifying, we get: 12 + 2b = 0. Solving for b, we find b = -6.
Now substitute the value of b into one of the original equations and solve for c. Choosing the first equation, we have: 2² + 2(-6) + c = 3. Simplifying, we get: 4 - 12 + c = 3. Solving for c, we find c = 11.
Therefore, the value of c is 11 (Option D).