Parabolas 

Designed by: Melanie B. Moorer   School: Dreher High School 

Grade Level: 11-12     Subject: Mathematics (Algebra III/Trigonometry)

Core Curriculum Objective: Find and graph equations of parabolas.

Overview: Students will work independently and in small groups to develop strategies to find and graph equations of parabolas and apply their knowledge in everyday situations. Students will use various instructional strategies such as: demonstrations, presentations, critical thinking, and deduction. As a culminating assessment, students will use a picture of a famous archway, such as the Golden Gate Bridge, London Bridge, the bridge at Grandfather Mountain, or even more locally - Cooper River Bridge, and draw a coordinate plain on them in order to find the equation of the parabola that forms the archway. 

Purpose/Essential Question: How do you find and graph the equation of a parabola? 

Time Frame: This lesson is designed for one ninety-minute class period. 

Resources and Instructional Materials:

Advanced Mathematical Concepts 
Glencoe/ McGraw-Hill 
936 Eastwind Drive 
Westerville, Ohio 43081-3329 
Pages 534-541 

Transparencies 

Overhead Projector 

Picture of famous archways

Rulers 

Graphing Calculators 



Bell-Work:  (work to be done when the student enters the class before the tardy bell) 

Have students copy the following formulas for the equations of a parabola off a ready-made transparency: 

For both equations: vertex: (h, k) and p is the distance from the vertex to the focus. 

Motivating the lesson: 
Have students draw a line and a point near the line on a sheet of paper. Ask them to find points that appear to be equidistant from the point and the line, to connect them, and to describe the resulting curve. The curve should look like a parabola. 

Work through the following teacher-led examples: 

1. Find the coordinates of the focus and the vertex and the equation of the directrix and the axis of symmetry for the parabola with the equation: 

2. Use a graphing calculator to graph:

3. The Tillman Company produces the Concave Perforated Antenna, which is a satellite dish made from aluminum with 2-millimeter perforations. The 
diameter of the satellite dish is 3 meters, and it has a f/D ratio of 0.278. Write 
an equation that models the shape of this dish. Assume that the vertex is at the origin and the parabola opens to the right. 

4. Write the standard form of the of the equation:

Then graph the equation. 

Activity One: 
Have students work independently on Worksheet A for 15 minutes. Then let the students get with their partner (already selected by the teacher when designating collaborative pairs) compare work and reach a consensus on what the correct answers are. After another ten minutes, randomly select student pairs to come up and find distances on the overhead for the class to see. 

For homework, give the students some problems similar to those on Worksheet A. 

Activity Two 
Students will receive the rubric for this lesson. In this activity, the students will demonstrate their ability to find and graph equations of a parabola by drawing a coordinate grid (demonstrated by the teacher) on a picture of a famous archway such as: the Golden Gate Bridge, London Bridge, the bridge at Grandfather Mountain, or even more locally - Cooper River Bridge. The student will find the equation of the parabola, then graph it on a piece of graph paper attached to the 
picture. The student will also include equations for the axis of symmetry and the directrix, as well as the coordinate of the vertex and focus. The teacher will evaluate the culminating assessment with the following rubric: 

Worksheet A 
Parabolas 
(Click here for a printable Adobe Acrobat version of this worksheet)

Name _____________________________________________________

Date __________________________________

For each equation, 

a. write the standard form, 

b. find the coordinates of the focus and vertex, and the equation of the directrix and axis of symmetry, and 

c. graph the equation. 

Write the equation of the parabola that meets each set of conditions. 

3. The parabola has its focus at (1, 3) and the vertex is at (1, 2)

4. The focus is at (2, 1), and the  equation of the directrix is  x = -2.