Key Features of Quadratic Functions

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Objective

SWBAT find several key features of a quadratic function including intercepts, turning points, and roots.

Big Idea

This lesson will serve as a summary of finding all key feature of a quadratic function.

Warm Up

3 minutes

In this lesson, I want my students to consider finding the coordinates of the vertex of a parabola to be one step in the process of finding all of the key features of a quadratic function. Since this is a synthesis day, I will have each student work on Today's Warmup independently for a few minutes. I want students in the mode of pulling things together in their own mind. After a few minutes, I will ask one student to post his/her work on the board. While he/she works, I will let the rest of the class compare their answers with a partner. I expect students to verify their answers with a partner and with the solution on the board. I will decide whether to have a class discussion based on the number of students whose answers are not correct.

 

Direct Instruction

15 minutes

Practice

17 minutes

After doing the first example on Parabola_Key_Features as a class, I plan to ask students to work with a partner on the other three questions.  I encourage students to use the graphic organizer from our work together as a resource.

As they work, here are some thing that I will be watching for:

  1. In #2, I want to make sure students are using the correct signs on values when substituting into the formula x=-b/2a.
  2. Also in #2, I will look to see if students successfully factor the trinomial. Many of my students struggle if they do not factor -1 as a greatest common factor (GCF).
  3. In Question #3 and #4, the expression does not factor with rational coefficients. My students will have to use either the quadratic formula or completing the square in order to use the equation to find the zeros of the function.

Closure

5 minutes

In my classroom, it seems like time always runs short at the close of a lesson.  With that said, I make sure not to rush today's closing activity. For today's Ticket out the Door I have students examine this list of_features independently. I ask each student to write down the features they are completely confident in finding on their own.  I tell students that these lists can be as long or as short as necessary.  Students can put their choices on a half sheet of paper with a line down the middle.  As students leave I collect this list as feedback of the general comfort level of the class as well as the specific needs of students in the class.