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.

Answer 1

The graph of y = -2x^2 is a downward opening parabola with its vertex located at the origin (0,0). As x increases, y decreases, creating a symmetric curve.

The graph of y = -2x^2 + 4 is also a downward opening parabola, but it is shifted 4 units up compared to the first function. Its vertex is at (0,4) and as x increases, y still decreases, but the entire graph is shifted upwards.

In conclusion, both functions have the same shape (downward opening parabola) but differ in their position on the coordinate plane (one is at the origin and the other is shifted upwards).