In 9th grade work and writing 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.
To graph the quadratic functions y = -2x^2 and y = -2x^2 + 4, we can start by creating a table of values and plotting points.
For y = -2x^2:
x | y
-2 | -8
-1 | -2
0 | 0
1 | -2
2 | -8
Plotting these points on a graph, we see that the graph is a downward-opening parabola, with the vertex located at (0,0).
For y = -2x^2 + 4:
x | y
-2 | 0
-1 | 2
0 | 4
1 | 2
2 | 0
Plotting these points on the same graph as the previous function, we see that this graph is also a downward-opening parabola, but it has been shifted upwards by 4 units. The vertex of this parabola is located at (0,4).
Comparing the two graphs, we see that they have the same shape as they are both downward-opening parabolas. The only difference is that the second function has been shifted upwards by 4 units, resulting in a different position on the graph.
In summary, the shape of the graphs of y = -2x^2 and y = -2x^2 + 4 are the same, but the position of the second graph has been shifted upwards by 4 units.