To graph the quadratic functions y = -2x^2 and y = -2x^2 + 4, we can use the standard form of a quadratic function y = ax^2 + bx + c. In this case, a = -2, b = 0, and c = 0 for the first function, and c = 4 for the second function.
1. Graph of y = -2x^2:
- The graph is a downward facing parabola.
- The vertex of the parabola is at (0, 0).
- The y-intercept is 0.
- The x-intercepts are at (0, 0) when y = 0.
2. Graph of y = -2x^2 + 4:
- The graph is a downward facing parabola.
- The vertex of the parabola is also at (0, 4).
- The y-intercept is 4.
- The x-intercepts are at (0, 4) and when y = 0, x = ±√2.
Comparing the two graphs, we can see that the second graph has been shifted upwards by 4 units compared to the first graph. The vertex of the second graph is higher than that of the first graph. Both graphs are symmetric about the y-axis.
Overall, the shape of both graphs is the same (a downward facing parabola), but their positions are different due to the constant term added to the second function.
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.v
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