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# Key Features of Quadratic Functions

Lesson 16 of 21

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

*40 minutes*

#### Warm Up

*3 min*

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.

#### Resources

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#### Practice

*17 min*

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:

- In #2, I want to make sure students are using the correct signs on values when substituting into the formula x=-b/2a.
- 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).
- 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.

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#### Closure

*5 min*

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.

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- LESSON 1: Overview of Quadratics-Essential Vocabulary
- LESSON 2: Quadratic Functions and Roots
- LESSON 3: Equations involving Factored Expressions
- LESSON 4: Solving Quadratics by Factoring-Day 1
- LESSON 5: Solving Quadratics by Factoring-Day 2
- LESSON 6: Applications of Quadratics Day 1
- LESSON 7: Simplifying Radical Expressions
- LESSON 8: Solving Quadratic Equations with Perfect Squares
- LESSON 9: Completing the Square Day 1
- LESSON 10: Irrational Zeros of Quadratic Functions
- LESSON 11: The Quadratic Formula-Day 1
- LESSON 12: Comparing the Three Methods of Solving Quadratics
- LESSON 13: Three Methods of Solving Quadratics and Word Problems
- LESSON 14: Identifying Roots and Critical Points-Need to Edit
- LESSON 15: Graphing Quadratic Functions Day 1
- LESSON 16: Key Features of Quadratic Functions
- LESSON 17: Sketching Polynomial Functions
- LESSON 18: Vertex Form of a Quadratic Function
- LESSON 19: Transformations with Quadratic Functions
- LESSON 20: Modeling With Quadratic Functions
- LESSON 21: Projectile Problems & Review