 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

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

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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