Choosing a Method to Find x-intercepts

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SWBAT determine which method (graphing, vertex form, or factoring) is most appropriate for finding x-intercepts given a quadratic function. SWBAT find a quadratic for two given x-intercepts.

Big Idea

Students take a step back from their work to examine a variety of quadratic functions and reflect on why they might choose one method over another.


7 minutes

I start today’s lesson will begin with a Curriculum Based Assessment on factoring:

Factoring 1

I use this CBA as a quiz or as a quick check-in to make sure students understand how to factor.  I set the timer for five minutes on this CBA and let students work on any of the problems on the page. I only give page one of this pdf.  After the timer goes off, I collect student work. I'll want to make sure to correct it before the next class so I can arrange for one-on-one or small group instruction for students who are still struggling.

DIFFERENTIATION:  Students who are ready for more advanced factoring can work on Factoring 2, a more advanced set of tasks.


45 minutes

The point of today’s lesson is for students to tie some loose ends together and begin finishing the unit on Quadratics. Students will work together in small groups and I may discuss their results with them as they work or gather everyone together at the end class.

The first activity asks students to explain Which Method they would use to find the x-intercepts of a quadratic and why. They are also asked to explain why they chose that method.  I will discuss this work as a whole group or in small groups as they finish when to use which method. I want to make sure students understand that the vertex method will always work for any quadratic.

The Find a Quadratic activity asks students to write equations for a quadratic function based on given x-intercepts. Students will then move on to Find a Quadratic.  Students will be given x-intercepts and be asked to write a quadratic with those intercepts.  I find some students will need help to write a function for three x-intercepts. I try to elicit from students that this will not be a quadratic and help them understand why.

Most students will write basic answers for their equations. For example, given the x-intercepts  x = 3 and x = 2, most students will write y = (x – 3)(x – 2).  I ask students ready for an extension to write this equation in standard form. I also try to elicit from students that this is not the only equation of a quadratic with these x-intercepts  I try to elicit from students what some other equations might be that have the same x-intercepts. Students should realize that any value of a with the same equation will work.


8 minutes

I give students time at the end of this lesson to reflect on their preferences for solving for x-intercepts.  I ask them to write an exit ticket responding to the following prompt:

Which method do you prefer to find the x-intercepts of a quadratic and why?