Monday, December 13, 2010

End Behaviors/Naming Polynomials!! =)

Linear Equations: 
y= mx+b 
1 degree
0 turns 

Domain - x values
Range - y values referred to as f(x)

When m is Positive: 
domain → +∞, range → +∞ (rises on the right)
domain → -∞, range → -∞ (falls on the left)












When m is Negative 
domain → -∞, range → +∞ (rises on the left)
domain → +∞, range → -∞ (falls on the right)












Quadratic Equations (parabolic equation)
y=ax² 
2 degree 
1 turn
(a+b)(c+d)
            
When a is Positive 










When a is Negative 

Identifying special situations in factoring

  • Difference of two squares
    • a2- b= (a + b)(a - b)
      • (x + 9)(x − 9)
      • (6x − 1)(6x + 1)
      • (x3 − 8)(x3 + 8)
  • Trinomial perfect squares
    • a+ 2ab + b2= (a + b)(a + b) or (a + b)2
      • x²-4x+4
      • 16x2 - 8xy + y2 = (4x - y)2
      • x²+6x+9
    • a- 2ab + b= (a - b)(a - b) or (a - b)2
  • Difference of two cubes
    • a3 - b3
      • 3 - cube root 'em
      • 2 - square 'em
      • 1 - multiply and change

        • Sum of two cubes
    • a3 + b3 
      • 3 - cube root 'em
      • 2 - square 'em
      • 1 - multiply and change
  • Binomial expansion

Quadratic equations: Circles, Parabola, Ellipse, Hyperbola


Quadtratic Equations:

How to identify quadratic equations:
ax² + bx + cy² + dy + e= 0

If there is an equation like 4x2 + 4y2 = 36 then it is a circle  because a=c. The a is 4 and the c is 4

If there is an equation like 2x2 + 4y = 3 then it is a parabola because a or c equals 0

If there is an equation like 4x2 - 4y2 = 12 then it is a hyperbola  because a and c have different signs.

If there is an equation like 4x2 + 3y2 = 25 then it is an ellipse because a is not equal to c, and the signs are the same.





--------This is an ellipse--------

Multiplying Matrices

There are 3 steps to multplying matrices.

1) Write a dimension Statement
2) Row x column and Sum x products
3) Repeat until complete

For this picture, you would have to repeat this process for the 2nd row x 4th column

Naming Polynomials:

--Number of turns is always 1 less than the degree.--

Degree:

0- Constant 
1- Linear
2- Quadratic 
3- Cubic
4- Quartic
5- Quintic 
6 to ∞- nth Degree 

Terms:

Monomial 
Binomial 
Trinomial 
Quadrinomial 
Polynomial 



domain → +∞, range → -∞ (falls on the right)
domain → -∞, range → -∞ (falls on the left)

domain → +∞, range → +∞ (rises on the right)
domain → -∞, range → -∞ (falls on the left)

Wednesday, October 6, 2010

Dimensions of a Matrix

  •    A matrix is a rectangular array of data. We would call it a table in using everyday terms, but it is not a table but a bracket.
  • The dimensions are listed as row x column, or n x m, where n represents the number of rows and m represents the number of columns.




EXAMPLES:

Tuesday, September 14, 2010

Error Analysis

The slope is 10/5 or 2. Not 10/1. Therefore the equation is wrong.
 the point, (1, -2) works for the first equation,but not the second. And it must work in both equations in order for it to be a solution.





#20-the line should be a dotted line
#21-shading should be below the line

Graphing Absolute Value Functions

  Graphing: y = a|x-h|=k
 When graphing an absolute value equation, your vertex will be (h,k).

*Vertical translations are shown by k:

*Horozontal translations are shown by h: it moves in the opposite direction of the indicated sign. if h is positive, then the graph moves left. if h is negative, the graph moves right.

*Vertical stretch of shrink is shown by a number in front of the absolute value signs.

Friday, September 10, 2010

Systems of Linear Equations

There are three types of solutions.
-Consistent:  
*independent: one solution: a point on a graph where two lines intersect. These lines have two different slopes.*dependent: same slope, same y-intercept.

These equations are the same line. The solution is written  as "All #s"-Inconsistent:
 
 Two lines with the same slope, but different y-intercepts. These lines are parallel.