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Quadratic Equations

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by

Charlie Helms

on 7 March 2014

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Transcript of Quadratic Equations

Trachette Jackson was born on July 24 , 1972 , in Monroe Louisiana . She attended a very large public high school, and took summer math-science honor classes at Arizona University . This is where she became interested in mathematics . Jackson received her B.S degree in 1994 , she also earned her M.S and Ph.D in 1996 &1998 . Her Ph.D thesis was entitle " Mathematical Model In Two Step Cancer Chemotherapy" . In 2006 , Jackson was appointed co-principal investigator of the National Science Foundation (NSF) . In 2008 , she become a full professor in Michigan's mathematics department . Trachette is the co-founder also the co- directer of the Mathematics Biology Research Group (MBRG) . The main reason for MBRG is to use math to gain better understanding of tumor growth and vascular structure of molecular and tissue levels .
Trachette Levon Jackson
(Tierra)
Quadratic Equations
A quadratic equation would be written as Ax^2 + Bx + C.
In order to get the answer that you are looking for, you would use the quadratic formula.


1. First a quadratic equation must be written down in its standard form. (Y=Ax^2 + Bx + C)
2. The values that are in place of A, B and C are put into the formula:
-b +- √b^2-4(a)(c)
-------------------
2(a)
In an equation like "-4x^2 + 3x + 5", -4 would represent the 'A' value, 3 would represent 'B' and 5 would be 'C'.
These parts of the equation are then put into the formula as:
-3 +/-√3^2-4(-4*5)
-----------------
2(-4)

Under the radical sign, the number would be 89. 89 is added to -3 and divided by '2(-4)'. Then 89 is subtracted from -3 and divided by '2(-4)'
1. Find the axis of symmetry by using the formula -b/2a.
2. Plug the axis of symmetry into the equation and the outcome will be the y value.
3. Write the vertex which would be the axis of symmetry for the x value,and the result of step 2 as the the y value.
4. Plot the coordinates of the vertex onto the graph.
5. Now find two other points. To do so use two different real numbers for the x value and then plug each one of those numbers into the equation to find the y value.
6. Plot the coordinates of the two points on the graph.
7. Now reflect the two points across the y-intercept axis.Then connect all of the points.

Step one-you write out your equation and set it to equal zero
Step two-subtract the constant from both sides (or add if it is needed.)
Step three- divide all of the terms by the leading coefficient if it is needed.
Step four- you take the B and divide it by two then square it: (B/2)². This will give you the C or constant value.
Step six- add the constant to both sides of the equation.
Step seven- square root the right side and factor out the left.
Step eight- set up the equation to where the left value is equal to plus or minus the right side value.This will give you two solutions.
Steps for completing the square
x²+6=27
(6/2)²=3²=9
x²+6x+9=27+9
(x+3)²=√36=6
x+3=6 x+3=-6
-3-3 -3 -3
3 -9
solutions:x=-3 or X=9
The quadratic formula can be used to solve any quadratic equation one might face. Though it does require a bit more effort than the other three techniques, the result is certain to be the correct answer, if the formula is done properly.
Solving Quadratic Equations Using the Quadratic Formula (Kayla)
Graphing quadratic equations is also a great strategy to use when trying to find the solutions. Like the quadratic formula, graphing quadratic equations also involves a series of steps to find the solutions if there are any.
With completing the perfect square you are forming the perfect square trinomial. Like with all of the other quadratic equations you need to use different steps in order to find the solutions.
Solving Quadratic Equations by Graphing
(Charlie)
Solving quadratic equations by completing the square.
(Skylar)
Example:
Steps to follow when Graphing
Example of a Graphed Equation
Using the Quadratic Formula
The Quadratic Formula in Use
By:Charlie Helms, Kayla Johnson, Tierra Rainge, and Skylar Shove
http://catalog.flatworldknowledge.com/bookhub/reader/128?e=fwk-redden-ch09_s05
Solving Quadratic Equations by Using Square Roots
(Charlie)
Not all quadratic equations can be solved using the other processes. Solving quadratic equations by using square roots is also a great strategy to use when trying to find the solutions of the equations if there are any.
Ways to Solve Equations by Using Square Roots
Other Ways for Them to be Solved
Example 1: x²-16=0
+16 +16
x²=16
x²=√16
x²=±4
Example 2: (x+2)²=9
x+2=√9
x+2=3 x+2=-3
-2-2 -2 -2
x=1 x=-5
Solving Quadratic Equations By Factoring
(Tierra)
There are many ways to solve a quadratic equation like taking square roots , graphing , completing the square and using the quadratic formula .I will show you how to solve a quadratic equation by factoring
Steps to solve a quadratic equation by factoring
(Tierra Rainge)
Examples
Step One ; find two numbers that multiply to give you AC and adds to give B

Step Two ; Rewrite the middle of the equation with the numbers that multiply to get the AC and add to get the B. Such as (x+2)(x+3)= 0
Step Four; Set the parentheses up to where they equal 0. x+2= 0 or x+3= 0.
Step Five; Subtract the number from 0, for each one.
Step Six; The solutions for this problem would be x= -2 or x= -3
When the equation is set up as x^2 =a then take the square root of both sides.
One you get the solution then you set it up as x=
Solutions for this equation would be a and -a.
a
Works Cited
http://www.math.buffalo.edu/mad/PEEPS/jackson_trachette.html
http://my.hrw.com/
http://commons.wikimedia.org/wiki/File:Plus_or_minus_symbol.svg
http://quizlet.com/23521007/radicals-and-logarithms-flash-cards/
http://www.csusm.edu/mathlab/documents/Completing%20the%20Square%20mf-r51.pdf
http://www.keepcalm-o-matic.co.uk/p/keep-calm-and-use-the-quadratic-formula-1/
http://gcdxy.wordpress.com/2012/08/10/why-many-students-hate-math-so-much/
http://www.someecards.com/usercards/viewcard/MjAxMy01M2I0Y2RkYzQ0ZTE4NGU1
http://catalog.flatworldknowledge.com/bookhub/reader/128?e=fwk-redden-ch09_s05
http://www.the-stickmen.com/comics/62/
http://www.zazzle.com/i_love_factoring_fridge_magnets-147240799919307323
x^2 + 3x + 2 = 0
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