Suppose that a ball that is thrown upward from a height of 5 feet at a speed of 40 feet per second. The height, h, of the ball after a time of t seconds can be calculated using the formula
h = -16t2 + 40t + 5.
An equation of this type is called a quadratic equation. Quadratic equations are useful for applications in geometry, physics, economics, and many other areas.
In this unit you will learn how to solve quadratic equations by various methods:
factoring and applying the zero product property
applying the principle of square roots
completing the square
using the quadratic formula
You will also learn how to use quadratic equations to solve some geometric applications including problems involving area and problems involving right triangles. Finally, you will learn how to graph quadratic equations on the coordinate plane.
Guiding Questions for Unit 8:
When and why should various methods of solving quadratic equations be used?
How can quadratic equations be used to solve application problems?
What is the relationship between a quadratic equation and its graph?
Lessons in Unit 8:
Lesson 1: Solving Quadratic Equations by Factoring
Lesson 2: The Principle of Square Roots
Lesson 3: Completing the Square
Lesson 4: The Quadratic Formula