Graph the quadratic functions y =- 2x7 and y =-2x? + 4 on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs.
(3 points)
To graph the functions y = -2x^2 and y = -2x^2 + 4, we can plug in some values of x to find the corresponding y values and then plot those points on a graph.
For y = -2x^2:
When x = -2, y = -2(-2)^2 = -2(4) = -8
When x = -1, y = -2(-1)^2 = -2(1) = -2
When x = 0, y = -2(0)^2 = 0
When x = 1, y = -2(1)^2 = -2
When x = 2, y = -2(2)^2 = -8
Plotting those points on a graph, we get a downward-opening parabola.
For y = -2x^2 + 4:
When x = -2, y = -2(-2)^2 + 4 = -2(4) + 4 = -4 + 4 = 0
When x = -1, y = -2(-1)^2 + 4 = -2(1) + 4 = -2 + 4 = 2
When x = 0, y = -2(0)^2 + 4 = 0 + 4 = 4
When x = 1, y = -2(1)^2 + 4 = -2(1) + 4 = -2 + 4 = 2
When x = 2, y = -2(2)^2 + 4 = -2(4) + 4 = -8 + 4 = -4
Plotting those points on the same graph, we get a parabola that is shifted up by 4 units compared to the graph of y = -2x^2.
Overall, both graphs are downward-opening parabolas, but the graph of y = -2x^2 + 4 is shifted up by 4 units compared to the graph of y = -2x^2.