Final answer:
The student needs to sketch the area enclosed by the parabola y = x^2, the line y = -x + 2, and the vertical lines x = 0 and x = 2 to visualize the intersection points that determine the enclosed area.
Step-by-step explanation:
The student is asked to sketch the area enclosed by the parabola y = x^2 and the lines y = -x + 2, x = 0, and x = 2. To do this, we need to plot each of these on the same coordinate system.
First, for y = x^2, we can start by plotting a few key points such as (0, 0), (1, 1), and (2, 4). This will give us a curve that opens upwards starting from the origin. Next, for y = -x + 2, plotting points where x is 0 and 2 gives us (0, 2) and (2, 0), which creates a straight line with a negative slope.
The vertical line x = 0 is simply the y-axis, and the vertical line x = 2 is a line parallel to the y-axis, passing through x = 2. The enclosed area is bounded by these lines and the curves.
To visualize this, imagine the parabola intersecting the line y = -x + 2 at two points, and those points also determine where the vertical boundary lines will cut through the parabola and straight line to enclose the area.