Quadratic Formula

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Objective

Students will be able to solve quadratic equations with the quadratic formula

Big Idea

Build the concept of the quadratic formula by deriving it from completing the square.

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. To stretch student's thinking this lesson’s Warm Up- Quadratic Formula, asks students to solve a quadratic equations using two different methods. 

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

Quadratic Formula

37 minutes

This lesson reviews an Algebra 1 standard, the quadratic formula, using the Algebra 2 extension of complex numbers.

We begin by reviewing the methods students currently have to solve quadratic equations which frames the day's lesson.  Please watch the Video Narrative for more information about this introduction.  At this point, I give the students the general form of a quadratic: ax2 + bx + c = 0 and have them complete the square with a, b, and c (Math Practice 7). This puts the quadratic formula in perspective so students don’t think it’s just some magical formula that somehow works.  Once they have had an opportunity to work on it, we will build it as a class to ensure that all students are on the same page.  We then solve several equations, with real and complex solutions, using the quadratic formula. 

The final goal for this lesson is to solve an area problem.  My contractor sent me a $3000 bill for fencing, priced at $15 per foot for a rectangular field that covers 1600 ft2. He said he hopes I’ll be happy with the project but forgot to tell me the dimensions of the fence he is building. He’s out of cell phone range on another building site, how can I figure out what dimensions he’s planning to install?  My goal for this problem is to give the students an opportunity to work on something that seems challenging at first (Math Practice 1) but is quite doable as they make start to look at the given information.  One scaffolding measure that may be useful is reminding the students to draw a diagram.  Another place students may struggle is figuring out the variable dimensions of each side of the rectangle so asking questions like "What would the length be if we call the width x?" or "What portion of the perimeter is just one length and one width?".  For the remainder of the class, we will discuss the solution and steps to the solution.  

Detailed presentation notes can be downloaded in the PowerPoint.

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 solve a quadratic equation using the quadratic formula.

Homework

This Assignment gives the students an opportunity to practice using the quadratic formula as well as solve several quadratic area problems (Math Practice 4).  

This worksheet was created with Kuta Software which is an amazing resource for any mathematics teacher.