Lesson 1: 9.1 Circles and Parabolas
Duration of Days: 5
Lesson Objective
1. Recognize a conic as the intersection of a plane and a double-napped cone.
2. Write equations of circles in standard form.
3. Write equations of parabolas in standard form.
4. Use the reflective property of parabolas to solve real-life problems.
How do you recognize each conic section and solve problems involving parabolas?
Conic section
degenerate cone
locus
circle
center
radius
parabola
directrix
focus
vertex
axis
focal chord
HSG-GPE. A. 1 - Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Use Khan Academy Resources
Students will use their prior knowledge of quadratic equations to study parabolas. Parabolas have many real-life applications, including satellite design, engineering, and astronomy.
Parabolas can be used to model and solve many types of real-life problems. For instance, a parabola can be used to design entrance ramp for a highway.
Students often become confused with the standard form of a parabola and the quadratic form because they are similar. Show students that these forms are different because the coefficient is written with the linear term in standard form and the squared term in the quadratic form.
Since this may be the first time students are introduced to parabolas with a horizontal axis of symmetry, some students may struggle with the standard form of the equation of a parabola.
Allow students the chance to construct a parabola using a piece of wax paper, a ruler, and a pencil. Have students draw a straight line (directrix) and a point (focus) on the wax paper. If the point is centered to the page, the parabola will be too. Then fold and crease the wax paper so that the line and the point intersect. Repeat this many times until the creases form the general shape of a parabola on your wax paper.
Use Common Assessments
Pre-Calculus with Limits