Final answer:
The equation y = -(x-2)² represents a parabola opening downwards with a vertex at (2, 0). To find the matching graph, plot several points by calculating y for chosen x values and then connect the points to reveal the parabola's shape.
Step-by-step explanation:
The student is asking for the graph that matches the equation y = -(x-2)². This equation represents a parabola that opens downwards due to the negative sign in front of the parenthesis. To plot this, we'll need to create a table of values by choosing different x values, inserting them into the equation, and calculating the corresponding y values. After plotting these points, we'll see the shape of the parabola. Its vertex, the highest point on the graph due to the downward opening, will be at (2, 0) since the equation is in the form y = -a(x - h)², where (h, k) is the vertex of the parabola.
Steps for Plotting:
- Choose x values around the vertex (2, 0).
- Calculate y for each x.
- Plot the points on the coordinate plane.
- Connect the points to form a parabola.