Question

Please help 50 points wrong answers will be reported

Answer 1

Answer:

A. $y=2\sqrt{x+4}+5$ is a translation of the parent function $y=2\sqrt{x}$ 4 units left and 5 units up

Step-by-step explanation:

Consider expression $\sqrt{4x+16}:$

$\sqrt{4x+16}=\sqrt{4\cdot (x+4)}=\sqrt{4}\cdot \sqrt{x+4}=2\sqrt{x+4}$

Hence, the function is

$y=2\sqrt{x+4}+5$

Consider the parent function $y=2\sqrt{x}$

The main translations:

• $y=2\sqrt{x-a}$ - a units to the right;
• $y=2\sqrt{x+a}$ - a units to the left;
• $y=2\sqrt{x}+b$ - b units up;
• $y=2\sqrt{x}-b$ - b units down.

Hence, $y=2\sqrt{x+4}+5$ is a translation of the parent function $y=2\sqrt{x}$ 4 units left and 5 units up