Quadratic Functions

If A and C have different signs (2x^2 -2y^2=6) then the equation is a hyperbola.

If A and C are not equal and they have the same signs (4x^2+6y^2=49) then the equation is an elipse.

Identifying Quadratic Functions

If you have an equation like 5x² + 5y²=25 The equation is a circle, because "a" is equal to "c"

If "a" or "c" equals 0 the equation is a parabola (for example: x² + 2y= 6)

Dimension Statements

Before you can begin to multiply matrices you need determine whether or not the matrices can be multiplied. To do that you must write a dimension statement. [3 4] [246][5 6] [7 8 9]
[11 3]The dimension statement for this would be 3X2 times 2X3.
The numbers on the inside must be the same in order to be able to multiply
The numbers on the outside tell what the dimension of the solution will be. In this particular problem, the solution will be a 3 X 3 matrix.

Identifying Matrices 3

This matrix is a three by three matrix but it is also known as a square matrix because it has the same number of rows and columns an identity matrix. An identity matrix has one going fom one corner to the next.

Identifying Matrices 2

This matrix is a three by two matrix. Three rows by two columns.

Identifying matrices

In order to identify a matrix you go row-by-column. Rows go across and columns go up and down. This matrix is a three by three matrix seeing as how it has three rows and three columns. BUt it is also a square matrix because it has the same numbers of rows as it does columns

Error Analysis 4

In problem 20 the shading is right but the line should be dotted.
In problem 21 the shading should be below the line

Error Analysis 3

The Issue With Problem 22 is that the line should be dotted. This is because the Problem is less than.
The problem with 23 is that the shading is incorrect. The shading shoul;d be above the line instead of under it.

Error Analysis 2

For this Problem We find that the error is the fact that the poin (1,-2) solves the first equation but not the second.

Error Analysis

In this problem your "x" value is increased by 5 therefore your slope should be 10/5 instead of 10/1. 10/5 can be simplified to a value of 2 so with this your formula should be y= 9+2x

Absolute value inequalities

In order to graph an absolute value inequality one must use the formula y=a|x-h|+k. The point (h,k) is your vertex. Point "a" determines if your graph moves up or down. If Point "a" is negative the graph will move down, if the point is positive the graph will shift upwards.Point k determines whether your grph will shift left or right. If point k is negative the graph will shift to the right and if k is positive the graph will move left.

Systems Of Equations

Consistent independent systems -have one solution where the cross.
Consistent dependent- these systems have infintely many solutions.
inconsistent- systems with no solutions (lines are paralell)