Naming Of Polynomials:
degree                 terms:
0 - constant          monomial
1 - linear              binomial
2 - quadratic        trinomial
3 - cublic             quadrinomial
4 - quartic           polynomial
5 - quintic
6 - nth

  

Postive linear equations

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

  

Negative linear equations

• 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)   

How to identify quadratic fuctions:

standard form of a quadratic:
ax² +bx + cy² + dy + e = 0
how to identify quadratic equations:
If a = c then the equation is a circle
If a does not equal c and the same sign then the equation is an ellipse
If a and/or c equals 0 the equation is a parabola
If a and c are different signs the equation is a hyperbola

Can you multiply Matrices?

To determine whether or not matrices can be multiplied you first have to write a dimensions statement.

Example of a dimensions statement:
[ 5  7 ]  [ 9 ]
[ 3  4 ]  [ 8 ]

Dimensions statement:
2 X 2 times 2 X 1

These matrices can be multiplied, so you would multiply row X column.
Then you get the sum of the products.
The numbers in yellow tell you that you can multiply the matracies.
The numbers in green tell you the size of the final matrix.

Dimensions of a Matrix

To count matrices you count row X column

This matrix is one row by three columns, so it is a 1 x 3 matrix.

This matrix is three rows by three columns, so this is a  3 x 3 matrix.
This matrix is a square matrix.

This matrix is three rows by two columns, so it is a 3 x 2 matrix.

This is another three rows by three columns, so this is a 3 x 3 matrix.
This is an identity matrix.

Error Analysis

• The x values are going up by five so the slope should 10/5 or 2 not 10. The equation of y = 9 + 10x does not work for this problem, because when you plug in the x values y does not agree with the numbers in the chart.

• The solution of (1,2) is not a solution of both equations. Meaning the soulution is not correct, in order for it to be correct it has to solve both problems. The solution solves the first equation, but not the second equation.

• On number 22 the graph is correct, but the line should be dotted instead of solid.
• On number 23 the grpah should be be shaded above instead of below.

• On number 20 the line should be dotted instead of solid.
• On number 21 the shading should be blow the line instead of above it.

Graphing absolute value equations

To graph an absolute value equation you must know that the parent function in y=|x| and looks like this when graphed; with a slope of 1/1:

The equation for this (and any absolute value equation) is y=a |x-h| + k.
Your vertex for the graph is your (h,k). The h value move the opposite direction, so if it was |x+4| the graph would move to the left 4 instead of right since it is inside the absolute value bars. A tells you if the V (a.k.a. the shape the equation makes when graphed) opens upward or downward. H moves your V left or right and k moves your V up or down.

Systems of Equations

Consistent/ Independent - when two lines intersect at one point on a graph; one solution
Consistent/ Dependent - same slope; same y-intercept; same line; solutions
Inconsistent - parallel; same slope; different y-intercept; no solution