Question

How would you describe the difference between the graphs of f(x)=2x^2 and g(x)=-2x^2

Answer 1

Please see the plot below.

Looking at the graph you can see that the function f(x) is a reflection on the x axis of the function g(x).

Explanation:

To plot the functions to compare graphs you should give values to x.

For example:

For
`f(x)=2x^(2)`, when x=-5:

`f(-5)=2*(-5)^(2)`

`f(-5)=2*(25)`

`f(-5)=50`

For
`f(x)=-2x^(2)`, when x=-5:

`f(-5)=-2*(-5)^(2)`

`f(-5)=-2*(25)`

`f(-5)=-50`

And giving different values you can construct the following table to plot the graphs:

x f(x)=2x^2 f(x)=-2x^2

-5 50 -50

-4 32 -32

-3 18 -18

-2 8 -8

-1 2 -2

0 0 0

1 2 -2

2 8 -8

3 18 -18

4 32 -32

5 50 -50

Please see the plot below.

Looking at the graph you can see that the function f(x) is a reflection on the x axis of the function g(x).