# How the does graph of y=-2x^2 differ from y=-2x^2 -2?

Nov 7, 2014

The graph of $y = - 2 {x}^{2}$ is a prabola pointing down, with its vertex at the origin (0,0). We can consider it as the "parent" function in this case. The graph of $y = 2 {x}^{2} - 2$ is another parabola- but it has gone through a transformation from the parent function. This transformation is of the "-2" attached at the end. It means that the graph of $y = - 2 {x}^{2}$ is shifted two units DOWN. The new vertex is at (0,-2).

Graphically, it looks like this:

This is the graph of $y = - 2 {x}^{2}$

Now, the graph of $y = - 2 {x}^{2} - 2$ is like the one above but shifted two units downwards, so it looks like this:

As a general rule for transformations, if you have something being added externally to an equation (like the minus 2 we had), the graph will be shifted vertically. If you are subtracting, you move DOWN by that amount of units. If you are adding, you move UP by that amount of units.

However, if you have something being added to the variable, then you shift the graph horizontally (For example,$y = 2 {\left(x - 2\right)}^{2}$). If you are subtracting a value from the variable, then you move the RIGHT that amount of units. So $y = 2 {\left(x - 2\right)}^{2}$) would be the original parent parabola but shifted to the right two units. If you are adding a value to the variable, then you move LEFT that amount of units.

Nov 7, 2014

Asnwer: The graph of $y = - 2 {x}^{2} - 2$ is shifted down by two.

When graphing an equation, adding or subtracting a fixed number will move the graph up or down.

In this case, the difference between the two equations is just $- 2$.

This is the graph of $y = - 2 {x}^{2}$:

This is the graph of $y = - 2 {x}^{2} - 2$: