Types of factoring

End Behaviors

The degree of an equation tells you how many times on the graph the line is going to turn.
The number of turns the line has will be one less than the degree of the equation.
I.e. a 3rd degree equation would have 2 turns
A monomial is a 0 degree constant.

A 1st degree equation is a linear equation and it is known as a binomial.

A 2nd degree equation is a quadratic equation and is known as a trinomial.

A 3rd degree equation is a cubic equation and is a quadrinomial.

A 4th degree equation is a quartic equation and is a polynomial.

A 5th degree equation is a quintic equation.

 

 

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When the term Domain is used it applies to X values

The term Range applies to the Y values 

• Domain → +∞, Range → +∞ (rises on the right)
• Domain → -∞, Range → -∞ (falls on the left)

• Domain → -∞, Range → +∞ (rises on the left)
• Domain → +∞, Range → -∞ (falls on the right)

• Domain → +∞, Range → +∞ (rises on the right)
• Domain → -∞, Range → -∞ (falls on the left)

• Domain → +∞, Range → -∞ (falls on the right)
• Domain → -∞, Range → -∞ (falls on the left)

Quadratic Functions

This is how to identify Quadratic Functions:
The standard Form is: ax² + bx + cy² + dy + e= 0
Circle Equation- A=C
So for example X²+Y²=9. So the center is at the origin. And the radius is 3.

Parabola- A or C = 0
For example: X²+4X+4. So the intercepts are at 2 on the x axis and 4 on the y.

Hyperbola- A or C has different signs from each other
For example: (X²/A²) - (Y²/B²) = 1
The two red lines are asymptotes. Or lines the hyperbola will continue to try to reach but will never reach.
Ellipse- A is not equal to C. However the signs are still the same.
For example: x²/16 + y²/4 = 1

Dimensions of a Matrix

                                                                    Row x coloum

The rows of a matrix are the numbers going horizontally.

[4 2 3]

The columns of a matrix are the numbers going vertically.

[2]

[3]

[5]

Multipying Matrices

2x(1 times 1)x9

The numbers show that the matrices can be multiplied, since the inside numbers are the same.

3)x1 times 1x(2

The outside numbers become the dimensions for the product matrix.

After you determined that the matrices can be multiplied, then you start to multiply them together. To do this, you would multiply the first row of the first matrix with the column of the second matrix. More specifically, you would multiply the first number of the first row on the first matrix with the first number of the first column of the second matrix. You then add the products together and thats the first number of the product matrix. You repeat this until all the numbers of both the matrices have been multiplied, giving you your product matrix.

Error Analysis

Should be a dashed line.

Should be shaded below

Error Analysis

     The line should be dashed.
           On the graph tit should be shaded above
                                                                                                    the line not below.

Error analysis

Hes not multiplying the x and the 10 together.

Need to check both of the equations to see if it is correct.

Absoluet value equation

y=a/x-h/+k
the H moves the equation up or down.
the K moves the equation to the left or right depending on the positive or negative.
the A determines the with of the graph.

3 Systems of Equation

Consistent/dependent
Same line ,same slope, same equation

3 Systems of Equation

inconsistent
Same slope, different starting position.
Never going to meet.

3 Systems of Equation

Consistent / Independent
Different slopes, cross at one point on the graph and then never cross again.