## Student Handout - parabolas.docx - Section 3: Explore: Deriving the Equation of a Parabola

*Student Handout - parabolas.docx*

*Student Handout - parabolas.docx*

# Parabolas

Lesson 8 of 13

## Objective: SWBAT find the equation of a parabola (vertex at origin) and graph parabolas.

## Big Idea: Guided examples of writing the equation of a parabola are followed by deeper reflection questions which students answer in their teams and share with the class.

*60 minutes*

Displaying page 2 of Flipchart - parabolas, students should copy the definition of a parabola into their Personal Dictionaries.

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I have decided to limit this lesson to parabolas that have a vertex at the origin only. I feel that my students quickly get overwhelmed with conic sections and find parabolas the most difficult. So in today’s lesson I really just wanted students to get a feel for how parabolas behave and how we can get a rough sketch of their graphs from the standard form equation. In tomorrow’s lesson, we will build on and look at parabolas with a vertex not at the origin.

In teams, students should complete the first section of the Student Handout - parabolas. I do expect my students to struggle a bit here.

Some of my students will struggle with the concept of how to square an absolute value expression. Students who have a solid understanding of what an absolute value means should have no problem. But I can see many of my students in their very systematic way of mathematical thinking just getting stuck here because they will wonder if they are allowed to square an absolute value. To help students through this struggle I will ask prompting questions like:

- What type of value will y+p always produce?
- Could we square the expression y+p?

If students are difficult to convince, I plan to have them test different cases. I would love to see students use their general form of y+p squared, y^2+2yp+p^2, to help test different cases where p is negative, y is negative, both are negative, and both are positive. My goal is to lead students to conclude that squaring y+p is the same as squaring the absolute value of y+p. I think it is important to allow students to struggle over this and develop their own understanding. It is not enough to leave them to remember how to square an absolute value. I want them to know how the standard form of a parabola is derived.

#### Resources

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To close out today’s lesson, I am going to ask students to complete the questions on pages 3-6 of the Flipchart - parabolas independently. I want to get a quick assessment of their current understandings. Before the closure questions, I am going to have a student pass out the Parabolas Summary. Students can use this to answer the closure questions.

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Cutting Conics
- LESSON 2: Name that Conic
- LESSON 3: Human Conics: Circles and Ellipses
- LESSON 4: Circles and Completing the Square (Day 1 of 2)
- LESSON 5: Circles and Completing the Square (Day 2 of 2)
- LESSON 6: Ellipses
- LESSON 7: Human Conics: Parabolas
- LESSON 8: Parabolas
- LESSON 9: Parabola Problem Partner Critiques
- LESSON 10: Hyperbolas
- LESSON 11: Non-Linear Systems of Equations
- LESSON 12: Conic Sections Test Review
- LESSON 13: Conic Sections Unit Test