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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Here are the graphs of y = -2x^2 (in blue) and y = -2x^2 + 4 (in red):
As you can see from the graphs, both functions are quadratic (meaning they have an x^2 term) and have a negative coefficient in front of the x^2 term (-2 in this case). This means that both functions will have a similar "bowl" shape.
However, the graph of y = -2x^2 + 4 (in red) has been shifted upward by 4 units compared to the graph of y = -2x^2 (in blue). This upward shift is called a vertical translation.
So, the main difference between the two graphs is their position. The shape of the graphs is the same, but the red graph is shifted up from the blue graph.