The graph of y = -2x^2 is a downward-opening parabola. It is symmetrical with respect to the y-axis and the vertex of the parabola is at the origin (0,0).
The graph of y = -2x^2 + 4 is also a downward-opening parabola, but it is shifted 4 units up compared to the graph of y = -2x^2. The vertex of the parabola is now at (0,4).
In terms of shape, both graphs have the same concave shape due to the negative coefficient of x^2. However, the graph of y = -2x^2 + 4 is shifted upwards compared to y = -2x^2.
Overall, the position of the graphs is different due to the constant term added in the second equation, causing a vertical shift of 4 units.
Graph the quadratic functions y = -2x2 and y = -2x2 + 4 on a separate piece of paper. Using those
graphs, compare and contrast the shape and position of the graphs.
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