Question #N454
The graph of the equation $y = (x-2)^2 + 1$ intersects the x-axis at two points. What is the sum of the x-coordinates of these two points?
A. -4
B. 2
C. 4
D. 6
Correct Answer is: C
The x-intercepts of the graph of an equation occur when y = 0. Substituting y = 0 into the equation gives us $0 = (x-2)^2 + 1$. Subtracting 1 from both sides, we have $-1 = (x-2)^2$. Since the square of a real number cannot be negative, there are no real solutions to this equation. This means the graph of the equation does not intersect the x-axis, and therefore there are no x-coordinates to sum. The answer is 4, which is the sum of the x-coordinates of the points where the parabola intersects the x-axis. This is incorrect because the graph does not intersect the x-axis.