## Week 11 PreCalc 11

This week we dived more into graphing by graphing quadratic inequalities in two variables. It’s basically the same thing as chp. 4 but we have to find out what side of the parabola the answers would come from. You do that by replacing x and y with numbers that aren’t on the line, (0,0) is the easiest so use that the most.

ex: ## Week 10 PreCalc 11

Semingly I didn’t learn anything new this week, I did forget most about how to do sequences and series. But after studying I remembered how to find $t_n$ or how to find $S_n.$

Example: But the one thing I had troubles with was finding $t_1$ when i am givin $t_4 and t_10$ but after figuring it out I found it pretty easy because all you have to do is find out how many numbers are in between 4 and 10 and then the rest is easy.

Ex: ## Week 9 PreCalc 11

This week in PreCalc 11 we learned how to take a word problem that looks like this, two number have a difference of 14, the product of those two numbers is the minimum, and we are able to find those two numbers.

We can do this taking a-b=14 and a*b=Minimum then isolating a in the subtraction equation the replacing a in the multiplication equation and then solve from there.

ex ## Week 8 PreCalc 11

This week in PreCalc 11 we learned about analyzing quadratic functions of the form $y=a(x-p)^2+q$. We learned how to find everything that we need to using this equation.

To find the vertex you need to do the same thing as before, you need to look inside the brackets and take that number for the x-axis then use the end number and use that for the y-axis. Then with the vertex you can find the axis of symmetry, then with the coefficient of x, you can find if it’s a minimum or maximum, if it opens up or down. You can find what it’s congruent to, as well as the intercepts and the Domain and Range.

Ex. ## Week 7 PreCalc 11

This week we looked a the discriminant and how to find how many roots there will be and what kind of root it will be.

You would need to use the equation $b^2$-4ac.

If the discriminant is above 0 then it will have 2 roots and be considered a distinct root, a real root and a rational/irrational root. If the discriminant is equal to 0 then it will have 1 root and will be considered as a equal root and a real root. If the discriminant is below zero then it will have 0 roots and will be considered to have no roots.

Ex:   ## Week 6 PreCalc 11

This week we learned about solving quadratic equations, I learned three different ways to do this.

The one that I really like to use is this one. I like this one because once I have my equation ( $4x^2+7x-1=0$), then I just have to plug the numbers in. Whatever the coefficient is for $x^2$ then that is a, then whatever the coefficient is for x then that is b and c is the extra number.

Ex: ## Week 5 PreCalc 11

This week we started factoring polynomial expressions. I learned how to take an equation like this $4x^2$-7x+3 and factor it into two binomials. I did this by using a box method and using CDPEU which stands for Common, Difference, Pattern, Easy and Ugly.

ex: I even learned how to take an even uglier expression and factor it.

Ex: I did this by changing (7x-5) to a and I did this to both of the (7x-5)’s.

## Week 4 PreCalc 11

This week in PreCalc we learned about solving radical equations. I learned how to take an ugly equation like this one 4= $\sqrt{-2x}$ +3 and simplify it.

Ex: To do so you have to state the restrictions of x(it’s mostly x>=0), then isolate x (if needed). Then you have to get rid of the square root by squaring it, then isolate x again. Then you have an answer. But you must check that it works by doing it again but by replacing x with what number you got and checking the restrictions.

Ex: ## Week 3 PreCalc 11

To change a mixed radical(5 $\sqrt{2}$) into entire radicals(\$latex \sqrt{1250}), this is what you need to do To change it from a entire radical to a mixed radical, this is what you do. ## Week 2 Pre Calc 11

This week I learned about Finite geometric series, I learned how to find $t_n$ and I also learned how to find the sum of $t_1$ to $t_n$.

To find $t_n$ you need $t_1$ and the common ratio.

So say I was trying to find $t_(15)$, so $t_1$=4 and the common ratio is 3. This is what you would do. Then to find the sum of all the 15 t’s, you would add $t_1$ + $t_2$ + $t_3$ +…etc. But the easier way to do it would be to do this. 