Answer:
D) [tex]y=4\sqrt{x+4}+3[/tex], because the graph is translated 4 left and 3 up.
Step-by-step explanation:
First, simplify the radical, do this by taking out [tex]\sqrt{16}[/tex]. So the equation turns into [tex]\sqrt{16} * \sqrt{x+4}[/tex], which can be simplified to [tex]4\sqrt{x+4}[/tex].
Then figure out the translations, to do this remember the form is [tex]y=a\sqrt{x-h}+k[/tex], where h is the x-value and k is the y-value. So, in this case, the x translation is -4 and the y is 3. It might seem like the x is positive, but remember since h is being subtracted you need to flip to sign to find the x translation. A negative x translation moves the graph left and a positive y value moves the graph up. Therefore, the answer is D.
