Question

Graph the quadratic function Y equals negative 2X squared and Y equals negative 2X squared +4 on a separate piece of paper, using those graphs can pair and contrast the shape of the position of the graphs

Answer 1

To graph the two functions, we first need to plot a few points and then sketch the parabolas.

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

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

Now, we can sketch the graphs on a separate piece of paper:
1) Graph of y = -2x^2:
This is a downward-facing parabola with vertex at the origin (0,0) and opens downwards.

2) Graph of y = -2x^2 + 4:
This is also a downward-facing parabola, but it is shifted up by 4 units. The vertex of this parabola is at (0,4) and it opens downwards.

Comparing the two graphs:
- Both graphs are downward-facing parabolas.
- The graph of y = -2x^2 is lower in position compared to y = -2x^2 + 4, due to the shift of 4 units up.
- Both graphs have the same axis of symmetry, which is the y-axis.

These comparisons show how the addition of a constant term affects the position of the graph of a quadratic function.