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

Answer 1

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.