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Quadratics
Given that a, b, and c are real numbers
Quadratic Equation in Standard Form
Where a, b, and c are real numbers
Why must we say a is not equal to zero?
NOT called a squaring function
Its graph is called a Parabola
Quadratic Function – a function that can be written in the following form
Where a, b, and c are real numbers
When dealing with a quadratic function:
•a is the coefficient on the x  squared term
•b is the coefficient on the x term
•c is the constant term with no variable
If we have a quadratic and do not see:
•an x term, what must b= ?
•a constant term, what must c= ?
Many ways to solve a quadratic
• Factoring
• Completing the square
• Quadratic Formula
• Technology
Factoring
You should already know how to do this
IF NOT, SEE ME.
You will not get through this course without finding a way to factor
Quadratic formula
Will work every time, even with imaginary roots
So, given:
Write what a = _____, b=______, c=___________
First, use the Discriminant to see what kind of answers to expect
PLUG in the values for a, b, and c and CHUG out an answer
It will tell us:
•we have 2 real answers if it is positive
•if it is a perfect square they will be nice
•if it is not a perfect square they will be ugly
•we have 1 real answer if it is zero and it will be pretty
•for now, if it is negative, there are no real answers
•later, if it is negative we have 2 imaginary answers
Sing along time!
If you did the Discriminant first this is real easy to
fill in
PLUG in the values for a, b, and c and CHUG out an answer
Completing the Square
Move the constant to the other side  
Insert blanks on both sides  
As long as the a coefficient =1, put (b/2)^{2} into both blanks 

The left side becomes (x and the terms in the parens )^{2} and the right becomes a number 

Move the constant to the other side and you Have the vertex form 

Where is the vertex? 
Technology
• Graphing  
• Programs  
• Apps 
Solving quadratics by Graphing
•Hit [y=] and type in the expression
•Hit [zoom][6] and see if you graph shows in the window
•If not you will need to work with your window
•See where the graph intersects the xaxis
•With the graph showing hit[2nd][calc][2] this is used to find a “zero”
•Your calculator will say, “Left Bound?”
•Move the cursor to the left of an intersection with the xaxis, hit [enter]
•Your calculator will say, “Right Bound?”
•Move the cursor to the right of the same intersection with the xaxis, hit
[enter]
•Your calculator will say, “Guess?”, hit [enter]
•Your calculator will say, “Zero?” and give you the x value that makes y=0
•This is a solution or a Zero , NOT a Factor
Programs
There are many programs of many types free on the web:
•Some are good
•Some are not
•If you use one you must be sure it works!
•General information is available on my website
•I have a limited number of Silver Graph links available
•You TI84 should have come wit a USB connection cord if you have not lost it
•Quadrat example
Applications
Your TI84 comes loaded with many applications
Ever tried Polysmlt?
Upgraded version Plysmlt2
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