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.

Answer 1

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.