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. (3 points)
To graph the quadratic functions y = -2x^2 and y = -2x^2 + 4, we first identify the vertex, axis of symmetry, and y-intercept of each function.
For y = -2x^2:
- Vertex: (0, 0)
- Axis of symmetry: x = 0 (y-axis)
- y-intercept: (0, 0)
For y = -2x^2 + 4:
- Vertex: (0, 4)
- Axis of symmetry: x = 0 (y-axis)
- y-intercept: (0, 4)
When we graph both functions on the same grid, we see that both graphs are downward-facing parabolas that open in the same direction. The graph of y = -2x^2 is positioned at the origin (0,0) and does not shift vertically, while the graph of y = -2x^2 + 4 is shifted vertically upwards by 4 units to the point (0, 4).
In summary, the shape of both graphs is the same, but the position of the graph y = -2x^2 + 4 is shifted upwards compared to the graph of y = -2x^2.