Unlocking Parabolas: Finding Equations from Three Points

Algebra 2 Grades High School 4:35 Video
Print Lesson Plan Watch Video

Lesson Description

Learn how to determine the equation of a parabola in standard form (y = ax^2 + bx + c) when given three points by solving a system of equations. This lesson focuses on using elimination to solve the system.

Video Resource

Equation of Parabola Given 3 Points (System of Equations)

Mario's Math Tutoring

Duration: 4:35
Watch on YouTube

Key Concepts

  • Parabola equation in standard form (y = ax^2 + bx + c)
  • Systems of linear equations (3x3)
  • Elimination method for solving systems of equations

Learning Objectives

  • Students will be able to set up a system of three linear equations given three points on a parabola.
  • Students will be able to solve a 3x3 system of equations using the elimination method.
  • Students will be able to write the equation of a parabola in y = ax^2 + bx + c form given three points.

Educator Instructions

  • Introduction (5 mins)
    Briefly review the standard form of a quadratic equation (y = ax^2 + bx + c) and remind students that three points uniquely define a parabola. Introduce the problem: finding the equation given three points and explain how to create a system of equations.
  • Video Viewing and Note-Taking (15 mins)
    Play the Mario's Math Tutoring video: 'Equation of Parabola Given 3 Points (System of Equations)'. Instruct students to take detailed notes, focusing on the steps involved in setting up the system and using elimination.
  • System Setup Practice (10 mins)
    Provide students with additional sets of three points. Have them practice setting up the system of three equations (without solving). Circulate and check for understanding.
  • Elimination Method Practice (15 mins)
    Have students work in pairs or small groups to solve the systems of equations they set up earlier. Encourage them to use the elimination method demonstrated in the video. Provide guidance as needed.
  • Wrap-up and Discussion (5 mins)
    Discuss the key steps in the process. Address any remaining questions or areas of confusion. Emphasize the importance of accuracy in arithmetic when using the elimination method.

Interactive Exercises

  • Parabola Equation Challenge
    Provide students with a worksheet containing several sets of three points. Have them find the equation of the parabola for each set of points. Increase difficulty gradually.
  • Online System Solver
    After solving a system by hand, students can use an online system of equations solver to check their answer. This promotes accuracy and provides immediate feedback.

Discussion Questions

  • Why do we need three points to define a parabola?
  • What are some strategies for choosing which variable to eliminate first?
  • What are some common errors to watch out for when solving systems of equations using elimination?

Skills Developed

  • Setting up and solving systems of linear equations
  • Applying algebraic concepts to geometric problems
  • Problem-solving and critical thinking

Multiple Choice Questions

Question 1:

What is the general form of a quadratic equation representing a parabola?

Correct Answer: y = ax^2 + bx + c

Question 2:

How many points are needed to uniquely define a parabola?

Correct Answer: 3

Question 3:

What method is primarily used in the video to solve the system of equations?

Correct Answer: Elimination

Question 4:

If you have three equations with variables a, b, and c, and you eliminate 'c' from the first two equations, what must you do next?

Correct Answer: Eliminate 'c' from the last two equations

Question 5:

After solving the system of equations, what do the values of a, b, and c represent?

Correct Answer: The coefficients in the quadratic equation

Question 6:

Which of the following is a step in the elimination method?

Correct Answer: Adding or subtracting equations to cancel out a variable

Question 7:

Given the points (0, 1), (1, 2), and (2, 5), which equation is set up correctly using the point (0,1)?

Correct Answer: 1 = a(0)^2 + b(0) + c

Question 8:

What is the first step in solving a 3x3 system of equations to find the coefficients of a parabola?

Correct Answer: Plug the x and y coordinates of each point into the standard form equation

Question 9:

Which best describes the elimination method?

Correct Answer: The process of removing a variable by adding or subtracting multiples of the equations

Question 10:

What is the final step once you find the value of a and b?

Correct Answer: Plug a and b into one of the original equations to solve for c.

Fill in the Blank Questions

Question 1:

The standard form of a quadratic equation is y = ax^2 + bx + ____.

Correct Answer: c

Question 2:

The _______ method is used to solve the system of equations in the video.

Correct Answer: elimination

Question 3:

A parabola can be uniquely defined by ____ points.

Correct Answer: three

Question 4:

When using the elimination method, the goal is to _______ one of the variables.

Correct Answer: eliminate

Question 5:

Before eliminating variables, you must first ________ each point to create a system of equations.

Correct Answer: substitute

Question 6:

After finding the values for a, b, and c, they are substituted back into the ____________ form of a quadratic equation.

Correct Answer: standard

Question 7:

To eliminate variables, you can multiply one or both equations by a ____________.

Correct Answer: constant

Question 8:

The first step in finding the equation of a parabola given three points is to _____________ each point into y = ax^2 + bx + c.

Correct Answer: substitute

Question 9:

The three points given will allow you to solve for the __________, a, b, and c.

Correct Answer: coefficients

Question 10:

Accuracy in _____________ is key to correctly applying the elimination method.

Correct Answer: arithmetic

Educational Standards

A2.A.1.7:Represent and evaluate mathematical models using systems of linear equations with a maximum of three variables. Graphing calculators or other appropriate technology may be used. A2.A.1.1:Use mathematical models to represent quadratic relationships and solve using factoring, completing the square, the quadratic formula, and various methods (including graphing calculator or other appropriate technology). Find non-real roots when they exist.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans