Solving Quadratic Equations
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.
Success Criteria: After completion of this module, learners will be able to
- Define a quadratic equation.
- Find the solutions of quadratic equations in the form ax2 + bx + c = 0 .
- 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.
- Numbers that are multiplied together.
- The answer when numbers are multiplied together.
Plan and/or Tasks
- Read the information above, including examples for finding solutions to quadratic equations.
- 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)
- How do you solve a quadratic equation?
- How many solutions are there to a quadratic equation?
- Use the two dimensional graph given on the resource page to find the solutions to: x2 -x-20 = 0.
- What is the relationship between the solutions to a quadratic equation and the x-axis?
- For what values of b is the expression factorable: x2 +bx +12?
- 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?
- Solve each equation:
a. x2 -7x-18=0
b . x2 -7x+12 =0
c. 5p2 -p-18 =0
d. 2b2 +17b +21 =0
- Explain something about quadratic equations to someone you know.
- Sketch the graph of problem 1a.
Ask your coach to look at your graph and answer. Be prepared to explain what you did.
Reflection on Learning:
- What strengths did you exhibit in learning about finding quadratic equations?
- In what areas would you like to improve your understanding of quadratic equations?
- What insight did you gain from your investigation of quadratic equations?