# How do you write the equation of the square root (radical) function that is shifted up 9 units, translated 7 units horizontally to the right, is reflected across the x-axis and is stretched 4 times that of its parent function?

Nov 25, 2017

 y = -4sqrt (x-7)) -9

#### Explanation:

You start out with the square root, so
$y = \sqrt{x}$

Add to the equation of the shift upwards
$y = \sqrt{x} + 9$

Add to the equation the translation
$y = \sqrt{x - 7} + 9$

Add to the equation the reflection
$- y = \left(\sqrt{x - 7}\right) + 9$
$y = - \left(\sqrt{x - 7}\right) - 9$

Add to the equation the stretch
$y = - 4 \left(\sqrt{x - 7}\right) - 9$