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.

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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.

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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.

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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.

 

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.

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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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Week 3 PreCalc 11

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}) into entire radicals($latex \sqrt[4]{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.

 

My arithmetic sequence

t_1 = 3, t_2 = 10, t_3 = 17, t_4 = 24, t_5 = 31.

So 3, 10, 17, 24, 31…

t_{50}?   S_{50}?

what I would do first is find out what is t_{50}.

t_n=t_1+(n-1)d

t_{50}=3+49(7)

t_{50}=3+343

t_{50}=346

Now I need to find S_50.

S_n=\frac{n}{2}(t_1+t_{50})

S_{50}=\frac{50}{2}(3+346)

S_{50}=25(349)

S_{50}=8725

So t_{50}=346 and S_{50}=8725.

Week 1 Pre Calc 11

This short week we learned about sequences but more importantly we learned how to get whatever number from the sequence.

Basically if t_1 was 5, then t_2 was 10, and t_3 then with what we learned I could find out what was t_{45}.

this is how.

This is what I learned this past week!