Reflecting simple parabolas
To reflect a parabola y=x2 through the x axis just place a negative sign in front of the x2.
y=-(x2) is a reflection of y=x2
Multiply everything by -1 and this gives you a reflection in the x axis only.
Think of a picture.
Example
Take y=x2 and reflect it
Reflecting y=x2 would give y=-x2
To prove this plot both parabolas.
1st y=x2
Try different values of x in the equation y=x2
| x=3 | then | y=32 | =9 |
| x=2 | then | y=22 | =4 |
| x=1 | then | y=12 | =1 |
| x=0 | then | y=02 | =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
Now plot y=-(x)2
NOTE:
-(x)2=-1×(x)2
Try different values of x in the equation y=-x2
| x=3 | y=-1×32 | =-9 | |
| x=2 | y=-1×22 | =-4 | |
| x=1 | y=-1×12 | =-1 | |
| x=0 | y=-1×02 | =-0 | |
| x=-1 | y=-1×(-1)2 | =-1 | |
| x=-2 | y=-1×(-2)2 | =-4 | |
| x=-3 | y=-1×(-3)2 | =-9 |
Plotted on the same graph this would look like:
