Solving Quadratic Equations

Why

The quadratic equation plays a pivotal part in mathematics and in real-life situations such as the invention of satellite television, the crafting of lens in your eye glasses, and even the creation of a wok for cooking.

Objectives

Learners will read the text about solving quadratic equations. Learners will learn to solve equations in the form ax2 + bx + c = 0.

Success Criteria: After completion of this module, learners will be able to

1. Define a quadratic equation.
2. Find the solutions of quadratic equations in the form ax² + bx + c = 0 .

Preknowledge

Learners should know how to factor polynomials.

Glossary

Quadratic

Quadratic is synonymous with parabolic.

Real Numbers

All positive and negative numbers and zero. The set of real numbers also includes all positive and negative fractions and all decimals that are repeating or non-repeating-- terminating or non-terminating.

Factors

Numbers that are multiplied together.

Product

The answer when numbers are multiplied together.

Resources

Please go to this Mahara page and download the file on Solving Quadratic Equations Resource

mahara.oeruniversitas.org/view/view.php

Plan and/or Tasks

Experience:

1. Read the information above, including examples for finding solutions to quadratic equations.
2. Using the first example, redo it on another piece of paper without looking at the answer. Then, check your work.

Key Questions (Critical Thinking Questions)

1. How do you solve a quadratic equation?
2. How many solutions are there to a quadratic equation?
3. Use the two dimensional graph given on the resource page to find the solutions to: x²   -x-20 = 0.
4. What is the relationship between the solutions to a quadratic equation and the x-axis?
5. For what values of b is the expression factorable: x²  +bx +12?
6. Name four values of b which make the expression factorable: x² -3x +b .
   7. Why is it impossible to have a linear trinomial with one variable?

Skill Exercises:

1. Solve each equation:
   a. x² -7x-18=0
   b . x² -7x+12 =0
   c.  5p² -p-18 =0
   d. 2b² +17b +21 =0
2. Explain something about quadratic equations to someone you know.

Problems:

1. Sketch the graph of problem 1a.

Validation:
Ask your coach to look at your graph and answer. Be prepared to explain what you did.

Reflection on Learning:

1. What strengths did you exhibit in learning about finding quadratic equations?
2. In what areas would you like to improve your understanding of quadratic equations?
3. What insight did you gain from your investigation of quadratic equations?

Self Assessment

What do you still need to learn about quadratic equations? What goals do you have for further investigation?