Question

Graph the quadratic functions y = -2x2 and y = -2x2 + 4 Using those graphs, compare and contrast the shape and position of the graphs.

Answer 1

To graph the quadratic functions y = -2x^2 and y = -2x^2 + 4, we will first plot some points and then connect them with a smooth curve.

For y = -2x^2:
When x = 0, y = 0
When x = 1, y = -2
When x = -1, y = -2

For y = -2x^2 + 4:
When x = 0, y = 4
When x = 1, y = 2
When x = -1, y = 2

Now, let's plot the points and draw the graphs:

Graph for y = -2x^2:
The graph of y = -2x^2 is a downward-opening parabola that passes through the points (0, 0), (1, -2), and (-1, -2).

Graph for y = -2x^2 + 4:
The graph of y = -2x^2 + 4 is also a downward-opening parabola but is shifted upward by 4 units compared to the first graph. It passes through the points (0, 4), (1, 2), and (-1, 2).

In comparing the two graphs, we can see that they have the same shape, as they are both downward-opening parabolas. However, the second graph is shifted upwards by 4 units compared to the first graph. This shift is due to the constant term of +4 added to the second function.

In conclusion, the two graphs are similar in shape but differ in position, with one being shifted upward compared to the other.