Square Root Functions

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Students will be able to graph the square root function using transformations.

Big Idea

Connect square root functions as the inverse to quadratic functions and an area model.

Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up- Root Functions, asks students to find the inverse for f(x) = x2. This is the starting place for the day's lesson and will lead students from quadratic functions naturally into radical functions.

I also use this time to correct and record the previous day's Homework.

Building a Square Root Function

37 minutes

We move into the main part of the lesson building off of the warm up, graphing the function on a coordinate plane.  We also look at the area model from the previous two lessons (1 and 2) to deepen and solidify their understanding of a square root function as the inverse of a square function.  We graph it, discuss its domain and range as well as how the concept of principal square root reinforces the concept of function (Math Practice 2). 

The next problem is an extension.  I give the students four equal squares and ask them to write a function that finds the side length of one square given the area of all of them (Math Practice 1).  I allow them time to work while I circulate providing assistance as needed.  Please see the PowerPoint for additional activity details details. 

We then graph several square root functions using the transformations the students already know and identify their domain and range.

The final question asks students to look at a new transformation f(x) = √(-x).  They discuss it and we compare its transformation to f(x) = -√(x) (Math Practice 7).  

Exit Ticket

3 minutes

 I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

Today's Exit Ticket asks students to graph a square root function using transformations. 


This homework asks student to solidify their understanding of transformations on square root functions by asking them to both graph and write these functions.  My Video Narrative talks about the final extension problem which asks students to compare a cube root function with a square root function (Math Practice 7).  

This assignment was created using Kuta Software, an amazing resource for secondary mathematics teachers.