graph the quadratic functions y = -2x^2 and y = -2x^2 + 4 on a separate piece of paper. Using
se graphs, compare and contrast the shape and position of the graphs.
After graphing both quadratic functions on a separate piece of paper, we can observe the following comparisons and contrasts in the shape and position of the graphs:
Similarities:
1. Both graphs are parabolas with a downward opening, which indicates that they have a maximum point. This is because the coefficient of the x^2 term in both equations is negative (-2).
2. Both graphs are symmetric about a vertical axis, called the axis of symmetry. In both cases, the axis of symmetry is the y-axis since there is no horizontal shift (both equations have no x term).
Differences:
1. The vertex (maximum point) of the two parabolas is different. For the first graph y = -2x^2, the vertex is at the origin (0, 0). For the second graph y = -2x^2 + 4, the vertex is at the point (0, 4).
2. The second graph y = -2x^2 + 4 is a vertical translation of the first graph y = -2x^2. The entire parabola is shifted 4 units upward along the y-axis. The shape of the parabolas remains the same; they only differ in position.
In summary, both quadratic functions have the same shape (downward-opening parabolas), but they differ in their vertical position on the coordinate plane. The second graph is shifted 4 units upwards compared to the first graph.