Learning Objectives:

__Math Tutoring on Graphing and Finding Equations of Transformed Square Root Functions__

The **square root parent function** is the simplest form of the **square root function, **or** f(x) =√ x. **

**Parent Function: f(x) = √x, x ≥ 0 **

**Vertical Translation: y = √x + d, **

**d ˃ 0:** shifts up **I**** d ****I** units and

**d ˂ 0:** shifts down **I**** d ****I** units.

**Horizontal Translation: y = √x – c, **

**c ˃ 0:** shifts to the right **I**** c ****I** units and

**c ˂ 0:** shifts to the left **I**** c ****I** units.

**Vertical Stretch and Compression: y = a√x, **

**1) ****I**** a ****I**** ˃ 1: vertical stretch, **

**2) ****I**** a ****I**** ˂ 1: vertical compression (shrink), **

**3) a ˂ 0: reflection in x-axis. **

**Horizontal Stretch and Compression: y = √bx, **

**1) ****I**** b ****I**** ˃ 1: horizontal compression: (shrink), **

**2) ****I**** b ****I**** ˂ 1: horizontal stretch, **

**3) b ˂ 0: reflection in y-axis.**

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**Hook Questions:**

*1. **What is meant by a parent function in a square root function?*

*2. **What is transformed square root function?*

*3. **What is Vertical or Horizontal Translation in a square root function? *

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