# Exploring Quadratics

#### 1 Hook

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

- Sits on the x-axis at x=5.
- Sits on the x-axis at x=-5.
- 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

- Remind students that the factored form of a quadratic equation is useful for finding the x-intercepts of the associated parabola.

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

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

- 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...

- get taller, but keep the same intercepts
- get shorter, but keep the same intercepts
- flip vertically

#### 4 Independent Practice

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

- 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.
- Students find the equation to the parabola, write it in standard form, and test it using Desmos.
- 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