Question

Graph the quadratic functions y = -2x2 and y = -2x2 + 4. Using those graphs, compare and contrast the shape and position of the graphs.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To graph y = -2x^2 and y = -2x^2 + 4, we can start by creating a table of values and plotting the points on a graph.

For the function y = -2x^2:
x | y
-2 | -8
-1 | -2
0 | 0
1 | -2
2 | -8

Plotting these points, we get a downward-opening parabola that passes through the points (-2, -8), (-1, -2), (0, 0), (1, -2), and (2, -8).

Now for the function y = -2x^2 + 4:
x | y
-2 | 0
-1 | 2
0 | 4
1 | 2
2 | 0

Plotting these points, we get a downward-opening parabola that passes through the points (-2, 0), (-1, 2), (0, 4), (1, 2), and (2, 0).

Comparing both graphs:
- Both graphs are downward-opening parabolas.
- The graph of y = -2x^2 is lower on the y-axis compared to y = -2x^2 + 4.
- The vertex of y = -2x^2 is at (0, 0), while the vertex of y = -2x^2 + 4 is at (0, 4).
- The graph of y = -2x^2 + 4 is shifted upwards by 4 units compared to y = -2x^2.

Overall, the graphs of y = -2x^2 and y = -2x^2 + 4 have the same shape but are shifted vertically by 4 units.