Answer:
reflection
vertical translation down 3
horizontal translation right 2
Step-by-step explanation:
Given
[tex]y = x^2[/tex] ---> Parent function
[tex]y = -(x+2)^2-3[/tex]
Required
All possible transformations
First, the parent function is reflected across the x-axis:
This gives:
[tex]y = x^2[/tex] [tex]==>[/tex] [tex]y =-x^2[/tex]
Next, it is translated horizontally right by 2
The rule is:
[tex](x,y)==>(x+2,y)[/tex]
So:
[tex]y =-x^2[/tex] [tex]==>[/tex] [tex]y = -(x +2)^2[/tex]
Lastly: it is translated vertically down by 3
The rule is:
[tex](x,y)==>(x,y-3)[/tex]
So:
[tex]y = -(x +2)^2[/tex] [tex]==>[/tex] [tex]y = -(x +2)^2 - 3[/tex]
