Mammoth Memory

Reflecting simple parabolas

To reflect a parabola `y=x^2` through the `x`  axis just place a negative sign infront of the `x^2`.

 `y=-(x^2)` is a reflection of `y=x^2` 

Multiply everything by`-1` and this gives you a reflection in the `x`  axis only.

Multiplying everything by -1 gives you a reflection through the x axis only 

Think of a picture.

 

Example

Take `y=x^2` and reflect it

Reflecting `y=x^2` would give `y=-x^2`

To prove this plot both parabolas.

 

1st `y=x^2`

Try different values of `x` in the equation `y=x^2`

 

`x=3` then `y=3^2` `=9`
`x=2` then `y=2^2` `=4`
`x=1` then `y=1^2` `=1`
`x=0` then `y=0^2` `=0`
`x=-1` then `y=(-1)^2` `=1`
`x=-2` then `y=(-2)^2` `=4`
`x=-3` then `y=(-3)^2` `=9`

 

And we plot this as

Plot the parabola on a graph

Now plot `y=-(x)^2`

 

NOTE:

`-(x)^2=-1times(x)^2`

 

Try different values of `x` in the equation `y=-x^2` 

`x=3`   `y=-1times3^2` `=-9`
`x=2`   `y=-1times2^2` `=-4`
`x=1`   `y=-1times1^2` `=-1`
`x=0`   `y=-1times0^2` `=-0`
`x=-1`   `y=-1times(-1)^2` `=-1`
`x=-2`   `y=-1times(-2)^2` `=-4`
`x=-3`   `y=-1times(-3)^2` `=-9`

Plotted on the same graph this would look like:

Reflect the parabola by minus x squared

 

 

 

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