Reflection: Developing a Conceptual Understanding The Parabola (Day 1 of 2) - Section 3: Developing the standard equation

 

This year I had an interesting comment come from some students that I had not expected. When we discussed the directrix some students asked if the directrix was an asymptote.  At first I was not sure where this idea was coming from but knew that I needed to clear this misconception.

After thinking I realized that students realized I had stated that that the parabola would not cross the directrix. Many students have a misconception that an asymptote is never crossed.  To help students understand the difference I began by discussing the asymptote of an exponential function we talked about how the function gets closer as closer to the asymptote as x goes to infinity (or negative infinity). I then asked if the parabola gets closer to the directrix at the ends (we were using an x^2 example) 

Understanding that the directrix is different than an asymptote is important since all conics can be defined using a directrix. It is also important for students to realize how a graph of a functions will get closer to the asymptote as x goes to infinity or as x approaches the vertical asymptote.  

  Directrix vs. Asymptote
  Developing a Conceptual Understanding: Directrix vs. Asymptote
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The Parabola (Day 1 of 2)

Unit 5: Conics
Lesson 3 of 13

Objective: SWBAT use different key features of a parabola to solve problems.

Big Idea: Why does the equation of a parabola have only one variable squared?

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2 teachers like this lesson
Subject(s):
Math, quadratic equations (Precalculus), distance formula, conic sections, parabola, paper folding, patty paper constructions, Conics
  40 minutes
parabola  psf
 
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