To graph y = -2x^2 and y = -2x^2 + 4 using a standard Cartesian coordinate system:
1. Assign values for x and compute the corresponding values of y for both equations.
2. Plot the corresponding points on the graph.
3. Connect the plotted points with a smooth curve.
Here's the graph of y = -2x^2:

Here's the graph of y = -2x^2 + 4:

As you can see from the graphs, the two quadratic functions have the same shape, but they are vertically shifted. The y-intercept of y = -2x^2 is 0, while the y-intercept of y = -2x^2 + 4 is 4. This is because the constant term in y = -2x^2 + 4 shifts the graph upward by 4 units.
10. Graph the quadratic functions y = -2x^2 and y = -2x^2 + 4 on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs.
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