To graph the quadratic functions y = -2x^2 and y = -2x^2 + 4, we can sketch the graphs by plotting a few points and then connecting them to form a smooth curve.
For y = -2x^2, when x = 0, y = 0. When x = 1, y = -2(1)^2 = -2. When x = -1, y = -2(-1)^2 = -2. So we have the points (0, 0), (1, -2), and (-1, -2) to plot the graph.
For y = -2x^2 + 4, we can add 4 to the y-values in the previous function to shift the graph up by 4 units. So the points become (0, 4), (1, 2), and (-1, 2).
Now we can connect the points to form the graphs. The graph of y = -2x^2 is a downward-opening parabola that passes through the origin and has a vertex at (0, 0). The graph of y = -2x^2 + 4 is also a downward-opening parabola, but it is shifted up by 4 units compared to the first graph. It passes through the point (0, 4) and has a vertex at (0, 4) as well.
In summary, both graphs have the same shape - a downward-opening parabola. The only difference is in the position, where the second graph is shifted up by 4 units compared to the first graph.
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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