on 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.
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on 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 
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But the one thing I had troubles with was finding 
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on 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.
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on This week in PreCalc 11 we learned about analyzing quadratic functions of the form 
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.
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on 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 
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.
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on 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 (
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on This week we started factoring polynomial expressions. I learned how to take an equation like this 
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I even learned how to take an even uglier expression and factor it.
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I did this by changing (7x-5) to a and I did this to both of the (7x-5)’s.
on This week in PreCalc we learned about solving radical equations. I learned how to take an ugly equation like this one 4=
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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.
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on This week in precalc we learned about simplifying radical expressions, I learned how to change mixed radicals into entire radicals and how to change entire radicals into mixed radicals.
To change a mixed radical(5![\sqrt[4]{2}](https://s0.wp.com/latex.php?latex=%5Csqrt%5B4%5D%7B2%7D&bg=ffffff&fg=000000&s=0 "\sqrt[4]{2}")
To change it from a entire radical to a mixed radical, this is what you do.
on This week I learned about Finite geometric series, I learned how to find
To find
So say I was trying to find 
Then to find the sum of all the 15 t’s, you would add 
