Answer:
A. [tex]y=2\sqrt{x+4}+5[/tex] is a translation of the parent function [tex]y=2\sqrt{x}[/tex] 4 units left and 5 units up
Step-by-step explanation:
Consider expression [tex]\sqrt{4x+16}:[/tex]
[tex]\sqrt{4x+16}=\sqrt{4\cdot (x+4)}=\sqrt{4}\cdot \sqrt{x+4}=2\sqrt{x+4}[/tex]
Hence, the function is
[tex]y=2\sqrt{x+4}+5[/tex]
Consider the parent function [tex]y=2\sqrt{x}[/tex]
The main translations:
- [tex]y=2\sqrt{x-a}[/tex] - a units to the right;
- [tex]y=2\sqrt{x+a}[/tex] - a units to the left;
- [tex]y=2\sqrt{x}+b[/tex] - b units up;
- [tex]y=2\sqrt{x}-b[/tex] - b units down.
Hence, [tex]y=2\sqrt{x+4}+5[/tex] is a translation of the parent function [tex]y=2\sqrt{x}[/tex] 4 units left and 5 units up
