Quadratic Functions

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

If you have an equation like 4x² + 4y²=36  The equation is a circle, because a=c
Example of a circle

If a or c equals 0 the equation is a parabola (for example: 2x² + 4y= 3)
Example of a parabola:

If a or c have different signs the equation is a hperbola ( for example: 4x² - 4y²= 12)
Example of a hyperbola

If you have an equation like 4x² + 3y²= 25 the equations is an ellipse, because a is not equal to c and the signs are the same
Example of an ellipse

Multiplying Matrices

Scalar multiplication is when you distribute the number outside the matrix to all the numbers inside the brackets.

To multiply matrices, you first need to write a dimension statement. The dimension statement basically states that the columns of the first matrix must match the rows of the other matrix

2x2*2x2

2x2 2x2

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

The bolded numbers become the dimensions of the new 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 that's 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.

3D Grapher! :)

http://www.livephysics.com/ptools/online-3d-function-grapher.php#add

(becauses Blogger hates the fact that I'm stealing code....)

Dimensions of a Matrix

The dimensions of a matrix refer to the number of rows and number columns of a given matrix.

The rows of a Marix go horizontally.

The columns of a Marix go vertically.

To find the dimensions of a matrix you must multiply the (number of rows x the number of columns). All three of these above matrices would be 2x3 (or 2 by 3).

Error Analysis

The value of x is going up by 5, so the slope should be 2 and not 10/1. By plugging in the points, the final equation should be solved. With this answer, y is not equal to 9+10x in the t-chart.

In order for a point to be the solution to a system, it has to solve both equations. So point (1,-2) solves the first equation, but not the second equation.

For problem #22 the shading is right, but the line should be dotted, not soild. For problem #23 the solid line is right, but the shading should be above it, not below it.

For problem #20 the shading is correct, but the line should be dotted not solid. For problem #21 the sloid line is right, but the shading should be below it not above it.

Absolute Value Euqations

Standard Form:
y = a|x – h|+ k

Parent Function:
y=|x|

y=a|x| (y=2|x|) Horizontal stretch by +2

y=a|x-h| (y=2|x-2|) Horizontal stretch by +2 and Horizontal shift +2

Systems of Equations

What are the types of Equation Systems?

Inconsistent - No solutions

Same slope, different y intercepts the lines are parallel

Consistent and Dependent - All Numbers (infinitely many)

Same slope, same y intercept

SAME LINE

Consistent and Independent - 1 solution (x, y)

different slopes