## 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

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

# Preknowledge

 Learners should know how to factor polynomials.

## Glossary

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

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

Problems:

1. Sketch the graph of problem 1a.

Validation: