Graph the quadratic functions
y = -2x^2 and y = -2x^2 + 4
on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs
The graphs of the two quadratic functions y = -2x^2 and y = -2x^2 + 4 are both downward-facing parabolas. However, the second function y = -2x^2 + 4 is shifted upward by 4 units compared to y = -2x^2. This shift essentially raises the entire graph of y = -2x^2 by 4 units.
Additionally, since the coefficient of x^2 in both functions is negative (-2), the graphs open downwards. The vertex of both parabolas is located at the point (0, 0) for y = -2x^2 and at (0, 4) for y = -2x^2 + 4. The vertex represents the maximum point of the parabola when the coefficient of x^2 is negative.
The graphs have the same shape and concavity, but the second graph is shifted vertically upwards from the first one. This shift changes the y-intercept of the second graph to (0, 4) compared to the y-intercept of the first graph, which is at the origin (0, 0).
In summary, the two graphs have the same concave shape but differ in their vertical positions due to the constant added to the second function.