Decoding Quadratics: Unlocking Solutions with the Discriminant

Algebra 2 Grades High School 9:44 Video
Print Lesson Plan Watch Video

Lesson Description

Master the discriminant of a quadratic equation to determine the number and type of solutions (real, imaginary, rational, irrational).

Video Resource

Discriminant of a Quadratic Equation - Determine Number and Type of Solutions

Mario's Math Tutoring

Duration: 9:44
Watch on YouTube

Key Concepts

  • Quadratic Equation: ax² + bx + c = 0
  • Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
  • Discriminant: b² - 4ac
  • Nature of Solutions: Real, Imaginary, Rational, Irrational

Learning Objectives

  • Students will be able to calculate the discriminant of a given quadratic equation.
  • Students will be able to determine the number of real and imaginary solutions based on the discriminant's value.
  • Students will be able to identify whether real solutions are rational or irrational based on whether the discriminant is a perfect square.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the quadratic formula and its components. Briefly discuss the graphical representation of quadratic equations (parabolas) and their x-intercepts (solutions).
  • Video Viewing (10 mins)
    Watch 'Discriminant of a Quadratic Equation - Determine Number and Type of Solutions' by Mario's Math Tutoring. Encourage students to take notes on the definition of the discriminant and its relationship to the solutions of a quadratic equation.
  • Guided Practice (15 mins)
    Work through the examples from the video together as a class. Emphasize the process of identifying a, b, and c, substituting them into the discriminant formula, and interpreting the result. Discuss the connection between the discriminant's value and the graphical representation of the parabola.
  • Independent Practice (15 mins)
    Provide students with additional quadratic equations to practice finding the discriminant and determining the number and type of solutions. Circulate to provide assistance and answer questions.
  • Wrap-up & Discussion (5 mins)
    Review the key concepts and learning objectives. Answer any remaining questions and preview the upcoming assessment.

Interactive Exercises

  • Discriminant Sort
    Provide students with a set of quadratic equations. Have them calculate the discriminant for each equation and then sort the equations into categories based on the number and type of solutions (two real, one real, two imaginary).
  • Parabola Matching
    Give the students the value of the discriminate and ask them to match the value to the correct graph of a quadratic equation.

Discussion Questions

  • How does the discriminant relate to the quadratic formula?
  • Explain how the sign of the discriminant determines the type of solutions.
  • What does it mean for a solution to be rational or irrational in the context of quadratic equations?
  • How can you determine the values of C for one real solution?

Skills Developed

  • Algebraic manipulation
  • Problem-solving
  • Critical thinking
  • Interpreting mathematical results

Multiple Choice Questions

Question 1:

What is the discriminant of the quadratic equation 3x² - 5x + 2 = 0?

Correct Answer: 1

Question 2:

If the discriminant of a quadratic equation is -4, what type of solutions does the equation have?

Correct Answer: Two imaginary solutions

Question 3:

Which of the following discriminants indicates that a quadratic equation has two distinct real and rational solutions?

Correct Answer: 4

Question 4:

The discriminant of x² + 6x + 9 = 0 is:

Correct Answer: 0

Question 5:

If the discriminant is positive but not a perfect square, the solutions are:

Correct Answer: Real and irrational

Question 6:

For what value of 'c' will the equation x² + 4x + c = 0 have one real solution?

Correct Answer: c = 4

Question 7:

Which quadratic equation has two imaginary solutions?

Correct Answer: x² + 2x + 5 = 0

Question 8:

What is the value of the discriminant for the equation 2x² + x - 3 = 0?

Correct Answer: 25

Question 9:

If b² - 4ac = 0, the graph of the quadratic equation touches the x-axis at:

Correct Answer: One point

Question 10:

Which of the following is the correct formula for the discriminant?

Correct Answer: b² - 4ac

Fill in the Blank Questions

Question 1:

The discriminant is the part of the quadratic formula under the ___________ sign.

Correct Answer: square root

Question 2:

If the discriminant is greater than zero, the quadratic equation has two __________ solutions.

Correct Answer: real

Question 3:

A discriminant of zero indicates that the quadratic equation has __________ real solution.

Correct Answer: one

Question 4:

If the discriminant is a negative number, the solutions are __________.

Correct Answer: imaginary

Question 5:

If the discriminant is a __________ __________, the solutions are real and rational.

Correct Answer: perfect square

Question 6:

The discriminant is calculated using the formula: b² - __________.

Correct Answer: 4ac

Question 7:

In the quadratic equation ax² + bx + c = 0, 'a', 'b', and 'c' are __________.

Correct Answer: coefficients

Question 8:

A quadratic equation with a discriminant of 16 will have two real and __________ solutions.

Correct Answer: rational

Question 9:

If the discriminant is not a perfect square, the real solutions are __________.

Correct Answer: irrational

Question 10:

The quadratic formula is x = (-b ± √(__________)) / 2a.

Correct Answer: b²-4ac

Educational Standards

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. A2.N.1.2:Simplify, add, subtract, multiply, and divide complex numbers.

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