This week we learned a new formula to help us find an angle or side length when we don’t have enough information. We call this the cosine law. All you do is chose the formula of which you need (side length or angle) and input the information that is given to you from the triangle.
This week we learned how to add rational expressions. First off you must know that expressions don’t have an equal sign so you are not trying to find a final answer, you are just adding and simplifying as much as you can. With that being said you must find a common denominator because you are adding. In this example the common denominator is the denominators multiplied. Since their are two (y-10) you don’t need to put it twice, only once. Now you are able to name the non permissible values. You want to do this first because if they were to change you know you have made an error. Then you multiply the numerator by the binomial that isn’t originally in the denominator. For this example the first fraction doesn’t have a (y-3) so you multiply the top by that because essentially that’s what you are doing to the bottom to get the CD. Then you do the same process with the other fraction. After this is done, you must solve the numerator, add them and simply. Leave the denominator factored as normal so you are able to see the non permissible values. Reminder that you do not add the denominators because like any addition question in fractions you only add the numerator once they have a CD.
This week in Pre Calc we learned about finding the non permissible values in a fraction with quadratics. To start off you must know what that means. Non permissible values are the values of x that would make the equation an error. We know that you cannot divide something by nothing therefore the non permissible values will be found in the denominator. Next you look at your denominator and think what value if x would cause this to equal zero. You must find them at the beginning of the equation before you begin simplifying. That is how you find the non permissible values!
This week in Pre Calc 11 I learned about absolute values and how to graph them. I learned that when graphing absolute values, the Y value can’t be negative; therefore the graph reflects and it is always positive. To start off, you graph the quadratic or linear like normal, but when you hit the X axis right before it turns negative, you reflect it, your graph will be opposite.
This week in pre calc we learned about substituting equations into other equations. Essentially it’s quite straight forward. All you must do is take the easiest equations out of the two and input that into the second equation. It doesn’t matter which one you do because you will get the same answer but it’s better to pick the easiest. So as showed in the picture below I decided to use y=-x+5 to put into 
This week in Pre-Calc 11 we learned about Inequalities. For example 
This week in Pre calc I relearned concepts of sequences and series. It was our first unit so I forgot some things I needed to go back and relearn. First I remembered how to find the common difference. If you have two terms that aren’t t1 all you do is plug your numbers into the formula t(large n) – t(small n) = the amount of space between the two(d). The picture below will demonstrate it further. 
Another thing is telling the difference between sequences and series and geometric and arithmetic. First off the difference between arithmetic and geometric is arithmetic has a fixed amount it’s adding by. For 2,4,6,8 the common differenceis +2. If it were geometric it is multiplying. For example 2,6,18,54 the common ratio is 3 because you are multiplying by 3 each time. For sequences and series, the difference is a sequence is just a pattern of numbers like 2,4,6,8 but a series is the sum of the numbers like 2+4+6+8.
Anither thing I forgot about was diverging and converging. All you need to know is if the ratio is bigger than 0 than it is diverging. If it is between 0 and 1 then it is converging.
This week we learned how to convert between each formula. If you are given the standard form and you want to get to general form you expand. If you are in general form and want to get to standard form you complete the square. Throughout the week we practiced how to covert the formulas to be able to use all the informational gives us. 
This week we learned the 3 different formulas you can use to collect info for the graph. The standard form can give you the vertex, can tell you the direction of opening, the line of symmetry and the vertical and horizontal translation. This information can help you with how to graph your equation. The general form gives you the y intercept and the direction of opening. And factored form shows you the x intercepts.
This week we learned how to apply our knowledge of quadratics into a graph. We started out with collecting all the info from the equation. And distributed this info in a table below. We learned that When we factor a quadratic equation that it give us the x intercepts because the graph crossed the x intercepts more than once. This is one of the main factors we learn in the previous unit. Now we are just applying it . 