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Quadratic Equations

Quadratic Equations

A quadratic equation in x is an equation that can be
written in the general form

ax2 + bx + c = 0

Where a, b, and c are real numbers

We can solve by several methods :
• By Factoring and setting each factor equal to 0
• Extracting Square Roots
• Completing the Square
• Using the Quadratic Formula
Using Your Calculator Wisely
Quadratic Equations - Factoring

Factor ax2 + bx + c = (Ax+B)(Cx+D) = 0

• Set each factor = 0. (Ax+B) = 0, (Cx+D) = 0
• Solve for x

Examples: To be worked in class
Quadratic Equations – Extracting Square Roots

• If you can manipulate the equation so that:

then, and or

Examples: To be worked in class

Quadratic Equations – Completing the Square

Given :  we can make it a " perfect square "


(Take ½ of b and square it)

If a the coefficient of x 2 is not 1, we divide both sides by a.

Examples: To be worked in class

Quadratic Equations – The Quadratic Formula

Given : we can use the quadratic formula


1. If , then there are two distinct solutions
2. If , then there is one repeated solution
3. If , then there are two complex solutions

Examples: To be worked in class

Quadratic Equations – Types of Solutions

Quadratic Equations – Solving By Graphing

A function must be entered into in order to obtain its graph.
Press the key. The resulting screen should look like this
 
Enter the equation in Y1

Then press graph

235 ft A Wrench Is Dropped From 235 ft up


Position from top
Initial position 235
Initial velocity 0 (If it is just dropped)

Number of Lawyers

L = .008t2 + 19.59t + 552.8,
t = 3 is 1983, L is in thousands,
What year does L =1000?
(That is 1 million Lawyers ?)

Taking a Shortcut
How much distance
Is saved?

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