Thursday, October 9, 2014

Week 9: How to make an equation using roots?, How to solve a system of equations that consist of a quadratic and a linear & Review

How to make an equation using roots?

Steps from eHow:

http://www.ehow.com/how_5828179_equation-given-its-roots.html

Simplified Steps:


1. Change each root into a factor by changing its signs

Example: roots: 3, -4, -4 ---> changed into factors--->( x - 3=0), (x + 4=0), (x + 4=0)

2. Multiply

Example: (x - 3) (x + 4)= x2 +4x – 3x – 12

(x2 +4x – 3x – 12)(x + 4)= x3 + 4x2+ 16x – 3x2 – 12x – 48

3. Simplify (combine like terms)

x3 + x2 +4x – 48


Video:


Class notes:


How to solve a system of equations that consist of a quadratic and a linear

There are two methods: Graphically and Algebraically

To solve graphically:

1.       Graph each function on the same coordinate plane

2.       Identify the points where the two graphs intersect.

3.       These points are the solution to the system of equations

 

Example 1:


1.       Graph each function on the same coordinate plane

 

2.       Identify the points where the two graphs intersect.

( -1, 4) and (3, 8)

3.       These points are the solution to the

system of equations

 

 

To solve algebraically:

1.       Set the functions equal to each other

2.       Solve for x

a.       Move everything to one side of the equation

b.      Factor

c.       Set each factor equal to 0

d.      Solve.

3.       The solution from step 2 is the x value of the solution of the system.

4.       Plug the x into either function to find the y.

5.       Write the solution as an ordered pair.

 

Example 2: 

1.       Set the functions equal to each other
2.       Solve for x
a.       Move everything to one side of the equation
 
b.      Factor
 
(x – 3)(x + 1) = 0
c.       Set each factor equal to 0
(x – 3) = 0     (x + 1) = 0
d.      Solve
x = 3             x = -1
4.       Plug the x into either function to find the y.
 
5.       Write the solution as an ordered pair.
(3, 8) and (-1, 4)

Video:
 
Review: See week 7, 8, & 9

Wednesday, October 1, 2014

Week 8: End Bx, Intercepts, Solving Polynomials



End Behavior: (Chart)
http://www.purplemath.com/modules/polyends.htm


Intercepts Video (Khan Academy):
http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing_with_intercepts/v/x-and-y-intercepts


X Intercept                                               Y intercept 
 
Steps to Solve                                               Steps to Solve
1.    Factor (find GCF)                                        1. Replace X with ZERO
2.    Set equal to ZERO                                      2. Simply/Solve
3.    Break apart & Set equal to ZERO

4.    Solve equation



Solving Polynomials: (Notes)

http://www.mathsisfun.com/algebra/polynomials-solving.html


Rational Root Theorem Video:
https://www.youtube.com/watch?v=-cZB1lyLlIM#t=35


Synthetic Division Video:



Putting it all together...