Lesson Plan

Using technology to quickly identify how quadratic equations are linked to changing parabolas. Todd B.
Classroom teacher
Lancaster Mennonite School
Lancaster, United States
My Subjects Math, Science
Objectives

Students will be able to...

• Write a quadratic equation from a graph.
• Predict how the shape of a parabola will change when it's quadratic equation changes.

Prior knowledge:

• Finding the roots of factorable quadratics
• Basic knowledge of Desmos
Subjects
Math

#### 1 Hook

Ask students to write the equation of a parabola which...

1. Sits on the x-axis at x=5.
2. Sits on the x-axis at x=-5.
3. Intersects the x-axis only at x=5, but opens in the negative direction.

Note: I use the Desmos iPad app in my classes. Do not be surprised if students have an incredible "need" to play with the Desmos app. I would plan on some time for students to explore the app the first time I introduce it.

#### 2 Direct Instruction Activity: Conversing
1. Remind students that the factored form of a quadratic equation is useful for finding the x-intercepts of the associated parabola.

2. Have students pair up and explain the role of the Zero Product Property in finding the x-intercepts.

3. Review the Zero Product Property by having a few students explain how to find the x-intercepts.

4. Ask: How can we use the Zero Product Property to write the equation from the parabola?

#### 3 Guided Practice

Ask students to find the equation of a parabola with x-intercepts at x=2 and -7. Students should work collaboratively either with shoulder partners or in groups of about 4 students.

Challenge students to make changes to the equation that make the graph...

1. get taller, but keep the same intercepts
2. get shorter, but keep the same intercepts
3. flip vertically

#### 4 Independent Practice

Our curriculum has this activity built in, but it would not be difficult to create it yourself.

1. Give students letters from people that are attempting to order a parabola. The letters may include such information as the x-intercepts and the vertex.
2. Students find the equation to the parabola, write it in standard form, and test it using Desmos.
3. Students should write a letter back indicating the correct equation for the requested parabola.

#### 5 Wrap-Up

Extend the lesson by giving students a "challenge letter". Present a letter from a customer who wishes to have a parabola with x-intercepts at (3,0) and (-5,0) AND vertex at (-1,4).

Point students back to the class objectives. If they know how to use the factored form of a simple quadratic to write an equation from a parabola, and can identify how to change the shape of the parabola by changing the coefficient of the factored form, they should be able to come up with the equation.

y=-0.25x^2 -0.5x +3.75