Graph the quadratic functions y equals -2x^2 and Y = -2x + 4 on a separate sheet of paper use those grass to compare and contrast the shape and position of the graphs

Answer 1

First, let's graph the quadratic function y = -2x^2.

To do this, we can create a table of values for x and y:

When x = -2, y = -2(-2)^2 = -8
When x = -1, y = -2(-1)^2 = -2
When x = 0, y = -2(0)^2 = 0
When x = 1, y = -2(1)^2 = -2
When x = 2, y = -2(2)^2 = -8

Now, we can plot these points and draw a smooth curve:

(graph will show a parabola opening downwards with vertex at (0,0))

Next, let's graph the linear function y = -2x + 4.

We can create a table of values for x and y:

When x = -2, y = -2(-2) + 4 = 8
When x = -1, y = -2(-1) + 4 = 6
When x = 0, y = -2(0) + 4 = 4
When x = 1, y = -2(1) + 4 = 2
When x = 2, y = -2(2) + 4 = 0

Now, we can plot these points and draw a straight line:

(graph will show a line decreasing with slope -2 and y-intercept at 4)

By comparing the two graphs, we can see that the quadratic function y = -2x^2 is a parabola that opens downwards with a vertex at (0,0), while the linear function y = -2x + 4 is a straight line with a negative slope and a y-intercept at 4. The quadratic function is symmetric about the y-axis, while the linear function has a constant rate of change.