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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 x-axis

•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 x-axis, hit [enter]
•Your calculator will say, “Right Bound?”
•Move the cursor to the right of the same intersection with the x-axis, 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 TI-84 should have come wit a USB connection cord if you have not lost it

•Quadrat example

Applications

Your TI-84 comes loaded with many applications

Ever tried Polysmlt?

Upgraded version Plysmlt2

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