Final answer:
To graph the parabola, create a table of values for x and y, plot the points, and connect them with a curve. To find the focus, directrix, and focal diameter, rewrite the equation in standard form, identify the values of p, h, and k, and use them to determine the focus, directrix, and focal diameter.
Step-by-step explanation:
Graphing the Parabola
Step 1: Start by creating a table of values for x and y.
Step 2: Substitute different values of x into the equation y = -2x² to find the corresponding values of y.
Step 3: Plot the points on a coordinate plane and connect them with a smooth curve.
Finding the Focus, Directrix, and Focal Diameter
Step 1: Rewrite the equation in standard form: y = 1/4p(x-h)² + k, where (h,k) is the vertex.
Step 2: Compare the standard form to the equation y = -2x² to identify the values of p, h, and k.
Step 3: The focus is located at (h, k+p) and the directrix is given by the equation y = k-p.
Step 4: The focal diameter is the distance between the focus and the directrix, which is equal to 4p.