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.
1. Graph of y = -2x^2:
- The graph is a downward facing parabola, with the vertex at (0, 0).
- The parabola opens downwards, indicating that the coefficient -2 causes the graph to be inverted.
- The graph does not intersect the y-axis.
2. Graph of y = -2x^2 + 4:
- This graph is also a downward facing parabola, but shifted up by 4 units.
- The vertex of the parabola is at (0, 4), which is higher than the vertex of the first graph.
- The parabola opens downwards, similar to the first graph, due to the negative coefficient -2.
- The graph intersects the y-axis at y = 4.
In comparison, both graphs have the same shape - downward facing parabolas. However, the second graph has been shifted up by 4 units compared to the first graph. Additionally, the y-intercept of the second graph is at y = 4, whereas the first graph does not intersect the y-axis. Overall, the position of the graphs differs due to the vertical shift in the second graph.