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