Parabolas and Review of Line-sanity!
Lesson 8 of 9
Objective: SWBAT determine the equation of a parabola given a focus and directrix and will also review key topics from line-sanity unit like, perpendicular and parallel lines.
Students will solve 2 warm-up questions that review parallel and perpendicular equations.
This activity will help students discover the relationship between a focus and directrix and discover that the locus of points equidistant from these is a parabola. Using patty paper (or a piece of lined paper), students will continuously connect the focus and directrix to create a parabola. This video shows a great example (at minute 1:15).
If you wanted to show students how to derive the parabola formula, teachers can show the Khan Academy video below but be prepared, this video is tricky and lengthy (almost 18 minutes long). I would recommend using the activity explained above as a way to teach and introduce focus, directrix and parabola rather than this algebraic approach.
Then, you can review with students the two formulas to write the equation of a parabola given the directrix and vertex. This worksheet also includes steps to follow to find the equation of a parabola as well as two examples.
Please also note that this topic can be covered in the circles unit as well if you are short on time. One possible lesson, in the circle unit, to add this activity in with is, Finding the Circle Formula.
Students can work independently or in small groups/pairs on this review assignment (MP 1). If you have time to review the answers for the practice test, then go for it! If not, there is time in the next day's class to review the practice test with students before taking the unit assessment.
Students should be encouraged to use their class notes to support their learning, and this review can be made into a student-centered activity. Students can be assigned questions to lead review on, and can present these to the class. This allows for student to practice using precise language (MP 6) and critique the reasoning of others (MP 3).
Students will review how to determine if lines are parallel, perpendicular or neither. This is a great review topic because it requires students to defend their answer by explaining, in words, how slopes relate to intersecting (or non-intersecting) lines.