Pre-Cal, Week 7

During Pre-Cal  this week i learned how to solve a chart with the properties of quadratic functions. To chart a quadratic equation you have to know how to tell when the table of value is showing a quadratic equation, instead of a linear equation. A linear equation in a table of value always has a y value (the output) that goes up or down by the same amount each time in the first differences. A quadratic equation in a table of value always has a y value that goes up or down by the same amount each time in the second difference. Below is a example of both a linear equation, and a quadratic equation charted.

When solving for quadratic functions, you should remember that the x intercept is always equal to y=0 and the y intercept is equal to x=0 (when solving). To find y you simply plug x into the given quadratic function. Below are some examples to visualize how I would solve for y using the table of values and quadratic function.

Pre- Cal, Week 6

This week in pre – cal, we got taugh 3 ways of doing an quadratic equation. 1. Factoring        2. Square rooting 3. Quadratic formula.  I will show all 3 ways of solving an quadratic equation. HINT : always trying to isolate the variable

1. Factoring

2. Square Rooting

3. Quadratic Formula

 

Pre-Calculus, Week 5

This week in Pre- Cal we went over Radical Equations and how to solve the equation. When solving a radical equation you need to move the variable to either the  left or right side of the = sign trying to isolate the variable. Also when solving a radical equation, when you have square root you would square it to get ride of the radical, make sure what you do to one side of the equations you do to the other and you would be left with the side without the radical and the other side would be squared.

Example:  make sure you are always checking that the variable would work if you put it back into the equation

I did learn this week that when Simplifying a Quotient of Radical Expression. You never want a radical in the denominator when you have an expression.

Step 1 : Multiply the numerator and the denominator by the radical in the denominator

Step 2: Then conjugate of the binomial denominator

Step 3: value the variable

Example:

Pre-Calculus, Week 4

When Multiplying a Radical with another radical you multiply the numerator with the numerator and the denominator with the denominator. If you have to equals like (7-\sqrt{6})(4+\sqrt{6})  you would use the foiling method or distributive property. Make sure you always simplify after you find the answer to make it as low as possible.

 

 

Arranging mixed radicals into descending order (greatest to least). The reason why i feel like this is important is because i get confused sometimes on whether or not i should change into an entire number or keep ir mmixedd. I find now that it is easier fofr me to change it into an entire number. In the example belong i’m going to show the method i use to solve arranging mixxed numbers to greatest to least.

Pre-Calculus, Week 3

This week in Pre- Cal 11 I learned about Absolute Value and Radicals.

Absolute Value of a real number is defined as the principle square root of the square of a number, Principle Square Root is always a positive number, Square of a number is \sqrt{25} = 5 but is you have \sqrt[2]{25}=5 it is always a positive number in absolute value so it would be for both \mid 5\mid . Absolute value is always the distance from zero.

When using Roots & Radicals: the \sqrt [root]{radicand} the number in front of the root is the coefficient. if you have a square root it is always a positive in the radicand and the index is always a 2. If you have a cute root it is either negative or positive in the radicand and the index is always 3. The higher roots can be \sqrt [4]{positive}  \sqrt [5]{positive/negative}  \sqrt [6]{positive}

 

 

Pre-Calculus, Week 2

One thing that I learned this week in pre Cal 11 is diverging and convergingDivering series means: there is no sum and it’s a finite or infinite geometric series; the formula used is S_n=\frac {a(r^{n}-1)}{r-1} . To find out if it is diverging you use r>1 or r<-1. Converging series means: there is a sum and it’s infinite or finite geometric series; the formula used is S_\infty=\frac{a}{1-r} . To find out if it is converging you use -1<r<1 or -1<decimals <1.

Example of Diverging series : 

Blue line : X |Y                     Orange line :  X | Y
1 | 4                                                1 |4
2 | 8                                               2 | 1.6
3 | 16                                             3 |0.64
4 | 32                                            4 | 0.256
5 | 64                                             5 | 0.1024
6 | 128                                           6 | 0.04096

Example of Converging series: 

purple line :  X | Y                       Red line : X | Y
1 | 4                                           1 |4
2 |-8                                          2 | -1.6
3 |16                                          3 |0.64
4 |-32                                        4 | -0.256
5 | 64                                         5 | 0.1024
6 |-128                                      6 | -0.04096

 



|