LEARN NC

CareerStart lessons: Grade eight

2.3 Working with parabolas

By Debbie Brooks, Peggy Dickey, and Jan Sullivan

Provided by CareerStart

Essential question: How can finding the vertex of a parabola be a useful career skill?

Learning outcomes

Students will graph quadratic functions and find the equation of the axis of symmetry and the coordinates of the vertex of the parabola.

Teacher planning

Materials needed

  • Fireworks worksheet (Includes answer key)
  • Graphing calculator
  • Overhead graphing calculator or TI Presenter
  • Graph paper transparency
  • Overhead projector
  • Colored pencils

Time required for lesson

Approximately 55 minutes

Activities

  1. Hand out the fireworks worksheet and read the problem with the students.
  2. Ask students to review the process of entering equations into the graphing calculator. Enter the given equation into the calculator. Review what the variables represent. Locate the meaning of the variables in the table. Have students copy the table down on their worksheet.
  3. Guide students in the process of making a graph for this scenario. Note: It is not necessary to have negative values for time (x). For the dependent variable (y-values) usually 10% of your range (maximum y value - minimum y value) allows your graph to have proper spacing. Use the table values to graph the quadratic function. Have students locate the highest height of the firework on the graph. You may choose to have students use colored pencils and draw a fireworks symbol to mark the peak.
  4. Have students solve the quadratic equation algebraically. Students need to refer to the equation x = -b/a in order to get the time for the maximum height (Remember that the x value represents time. Once students have solved for x, have them refer to their graphing calculator table to locate the y value that corresponds to the x value, which is the value for the maximum height). Have them locate the maximum height on the graph on the graphing calculator either by taking or trace [scroll down to maximum]).
  5. Ask students what factors could affect the maximum height of the fireworks. (e.g. wind, rain, angle at which the fireworks were released, dysfunctional fireworks, etc.)
  6. Conclude the lesson by brainstorming other careers that may use quadratic functions. Examples might include architects and engineers in designing bridges and archways, designers of baseball fields (homerun height of the back wall), firefighters, pyrotechnicians, event planners, landscapers designing sprinkler systems, sports personnel, field goal kickers, golfers, divers. For more specific information, see “Career Information” below.

Career information

Career information comes from the Bureau of Labor Statistics’ Occupational Outlook Handbook.

Landscape architects
Landscape architects design parks, playgrounds, and the outside areas around buildings using plants, flowers, trees, walkways, fountains, and water features for use and enjoyment. Some landscape residential yards that may need sprinkler systems for watering the grass and other plantings. Because the water in the arc of a sprinkler forms a parabola, quadratic equations can be used to determine the most efficient placement of sprinklers.

  • Education: Bachelor’s or master’s degree in landscape architecture
  • Pay: $45,800 - $77,600
  • Growth: Faster than average; 16% increase over the next 10 years
Civil engineers
Civil engineers design roads, tunnels, bridges, dams, and buildings. Many of these structures contain arches in their design and need to be able to withstand any weather, including hurricanes, as well as other natural disasters like earthquakes. Engineers must examine the height and the length of the arches that form parabolas to ensure each arch has the strength necessary for the designed structure.

  • Education: Bachelor’s degree in engineering
  • Pay: $59,000 - $94,500
  • Growth: Faster than average; 18% increase over the next 10 years

North Carolina curriculum alignment

Mathematics (2004)

Grade 9–12 — Algebra 1

  • Goal 1: Number and Operations - The learner will perform operations with numbers and expressions to solve problems.
    • Objective 1.02: Use formulas and algebraic expressions, including iterative and recursive forms, to model and solve problems.
  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.02: Graph, factor, and evaluate quadratic functions to solve problems.