Quadratic Equations
Quadratic Equations A quadratic equation in x is an equation that can be written in the general form ax^{2} + 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 ax^{2} + 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


Quadratic Equations – Completing the
Square Given : we can make it a " perfect square "


Quadratic Equations – The Quadratic
Formula Given : we can use the quadratic formula
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


235 ft  A Wrench Is Dropped From 235 ft up


Number of Lawyers L = .008t^{2} + 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 
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