Graph the quadratic functions y = -2x2 and y = -2x2 + 4 on a separate piece of paper.
I apologize, but as a text-based AI, I cannot draw or create visuals. However, I can describe how the graph of these quadratic functions would look like.
1. Quadratic Function: y = -2x^2
The graph of this quadratic function is a downward-opening parabola, as the leading coefficient (-2) is negative. The vertex is the highest point of the parabola, and it lies on the y-axis.
The vertex can be found by using the formula x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, a = -2 and b = 0, so the x-coordinate of the vertex is x = -0/(-2) = 0.
To find the y-coordinate of the vertex, substitute the x-coordinate into the quadratic function: y = -2(0)^2 = 0. Therefore, the vertex is (0, 0).
Since the coefficient of the x^2 term is -2, the graph will decrease rapidly as x moves away from the vertex. The graph will be symmetric about the y-axis.
2. Quadratic Function: y = -2x^2 + 4
This quadratic function is similar to the first one, but with a positive constant added. The additional +4 shifts the graph vertically upwards by 4 units.
The vertex remains the same at (0,0). The graph will still be a downward-opening parabola, but it will be shifted upwards by 4 units.
As x moves away from the vertex, the graph will still decrease rapidly, but it will be shifted up by 4 units compared to the first quadratic function.
Remember, these are just verbal descriptions. If you wish to accurately visualize the graphs, it may be best to graph them on a graphing calculator or using software like Desmos.