# Week 6 – Discriminant

Exp. $5x^2+4x-9$

a=5
b=4
c=-9

Put these values into the $b^2-4ac$ part of the quadratic equation.

$4^2-4(5)(-9)$

16-4(-45)

16–180

16+180=196

In this case the discriminant is positive so there would be 2 solutions for the quadratic equation. If it were to be negative there would be no solution and if it was equal to zero their would be one.

# Week 5 – Factoring Polynomials

Factoring is writing an expression in simpler form (UNLESS STATED IT’S NOT SOLVING ). To factor polynomials there are a few steps to take:

1. C-common (GCF)
2. D-differences of squares (BINOMIALS!)
3. P-pattern? (TRINOMIALS)
4. E-easy ($1x^2$)
5. U-ugly ($ax^2$)

Binomial exp.

$4x^2$-16\$

What’s common? 4

4 ($x^2-4$)

Is it a difference of squares (Binomial)? Yes

4(x-2)(x+2)

(x-a)(x+a) is a conjugates because if you foil it the middle terms will cancel so that you can have a binomial.

= $x^2 -a^2$ (this only works if you are subtracting) $x^2$-49 = (x-7)(x+7)

Trinomial exp.

$3x^2 -9x +6$

What’s common? 3

$3(x^2 -3x+2)$

Is it a difference of square? No

Does it have a pattern? Yes

$x^2$, x, #

Easy? Yes

$3(x^2 -3x+2)$

Now you figure out _x_=2 but also _+_=-3

-1x-2=2 and -1+-2=-3

3(x-1)(x-2)

Ugly Factoring exp.

$3x^2 +7x+4$

Anything common? NO

Difference of squares?Binomial? NO

Pattern? Yes

Is it easy? No

So you have to do ugly factoring aka box method!

You take the first term and the last term and put them in a box

$3x^2$ | #

#          | +4

Then you multiply them $3x^2 x4= 12x^2$

Then you find all the factors the would equal $12x^2$

1x-12x
2x-6x
3x-4x

Out of these factors pick the one that when added together equal term b.

7x=4x+3x

Then add these into the box,

$3x^2 | +4x$

+3x       | +4

Then find what’s common for the top row, bottom row, left column and right column.

Top row: 1x
Bottom row: +1

=(1x+1)

Left column: 3x
Right column: +4

=(3x+4)

(1x+1)(3x+4) would be the factored version of $3x^2+7x+4$

Recall for adding and subtracting variables, you can only add and subtract like terms.

Exp:

5x -4y +11x -y =

5x+11x       -4y-y

=16x-5y

For adding and subtracting radicals, you combine the coefficients, ONLY WHEN THE RADICAND AND INDEX OR THE SAME!

Exp:

$8\sqrt[3]{8}-9\sqrt[3]{8}+2\sqrt[3]{8}$

=$1\sqrt[3]{8}$

# Week 3 – Absolute value of a Real Number

“The absolute value of a real number is defined as the principal square root of the square of number.” This just means the absolute value of a real number is the square root of a squared number ex: $\sqrt{(5^2)}=5$ or $\sqrt{(-5^2)}=5$ Radicand after squaring and then square rooting (the absolute value of a real number) must be positive so you can find the absolute value of a negative or positive number.

EXP: |-6|=6

|6|=6

|7-2|=5 (if there’s an equation is in the brackets, you must solve before finding the absolute value)

# Week 2 – Geometric Sequences

To find a specific term in a geometric sequences you must have a sequence to work with, the find the common ratio which would be $\frac {t_n}{t_{n-1}}$ . After you find the common ratio and find $t_1$, you can fill in the general equation and then let the equation do the math!

2, 4, 8, 16, 32 Find $t_{11}$

$t_n=ar^{(n-1)}$

$t_{11}$= 2x $2^{11-1}$

$t_{11}$= 2x $2^{10}$

$t_{11}$= 2×1024

$t_{11}=2048$

# Week 1 – My Arithmetic Sequence

Sequence: 21, 27, 33, 39, 45…

$t_{50}=?$
$t_n=t_1+(n-1)d$
$t_{50}=t_1+(n-1)d$
$t_{50}=21+(50-1)6$
$t_{50}=21+(49)(6)$
$t_{50}=21+294$
$t_{50}=315$

$General Equation for t_n$
$t_n=t_1+(n-1)d$
$t_n=21+(n-1)6$
$t_n=21+6n-6$
$t_n=6n+15$

$S_{50}=?$
$S_n=\frac{n}{2}(t_1+t_n)$
$S_{50}=\frac{50}{2}(21+315)$
$S_{50}=25(21+315)$
$S_{50}=(25)(336)$
$S_{50}=8 400$

# Nature vs. Nurture

In the debate of nature versus nurture many would consider nature to be the more influential factor; but after analyzing and discussing the short story I Stand Here Ironing written by Tillie Olsen many would be persuaded into thinking that nurture is the most influential factor in growth and development. The story takes place during the great depression and tells the story of a mother and daughter with a destructive relationship. The story highlights Emma who was a happy and loving child but as she grew up she became more worried teenage. Nurture is the more influential factor in the development because whether environments are good or bad they shape and have long lasting effects. As seen in Emma who started as a loving and happy child full of life. Her home life was fine; her mother was a teen mom during the depression, the father left which made the mother have to go to work to provide. Emma had to be watched by the neighbours who didn’t appreciate her like her mother. This plays a part of the environment, being with people who don’t exactly want to take and be with someone else will play into insecurities of that person because they will question if they did anything wrong to be treated that way. Seeing this, children who’s parents leave them in the care of others tend to development issues with insecurities and abandonment. Also a few times a year, Emma would go to her father’s home because her mother had to work. Given the information when she came back she appeared more thin and worried. Emma also didn’t want to go to school because the teacher wasn’t kind and because school is such a big thing for a kid’s life and all their friends are there, Emma didn’t want to go and begged her mom to keep her at home. Emma loved when her mom was home but when her mom started dating a guy and she had to stay home alone, she became very paranoid. She left the door open so her mom could come home faster which is not a safe thing to do and the destroyed a clock because she heard it talking. This shows major flawless in the mother’s ability to care and rise her daughter in safe environment. In the arrival of her mom’s new husband and baby, Emma begins to show signs of jealousy and question why her mother didn’t give her as much attention as the child. During the night Emma would cry out for her mom but her mom never came and proceeded to yell for her to go back to sleep. Later in the night when the mother has to check up on the baby, she goes to check on Emma and she would tell here to go away. She is finding other ways to selfheal and she thinks that her mom won’t come when she needs her.

# September Paragraph

Students that attend public schools should learn about world religions because discrimination starts at a young age, it helps you understand current events and it plays a huge part in history. Teaching kids as young as 4 or 5 about world religions in simple terms will make them more open to different religions and people. Hopefully in doing so it will limit discrimination when they are older. When we teach something to kids, good or bad, they are heavy influenced by adults and remember certain things till they are older. If we teach them at a young age and set a good example for them we could potentially prevent future discrimination of religion, race and sexuality. They learn to be more open minded and accepting to all. Informing children about religions will help them in the future to better understand world events. Many positive and negative events are based on different religions or races. They will be educated to have more understanding of the points of views in the situation or just understand the situation as it is. Religion not only plays apart in today’s current events but also history which continues to influence today’s. If they know about religions think can fully understand the different components of history. Instead of saying just it was the Christians against the Jewish, they will fully understand each religion, the similarities, the differences and what they each want for each other. Most fights for land and wars were based on religion, race and region. In conclusion teaching world religions in public schools will help limit discrimination, help children understand current events and help them finally understand history.

# Shakespeare’s Authorship

(Shakespeare’s grave in Stratford-Upon-Avon.)

I think there is a lot of ‘evidence’ that shows that Shakespeare did not write all of his works, I think he wrote them all and the movie shows a very bias point of view. How can we assume he only wrote within a certain amount of time when we don’t even know his actual birthday. Maybe he learnt when  he acted or when he was very young, we have no records supporting either side. The movie is over analyzing his life and his works, even if he didn’t write his plays; he’s dead and his name is already on the plays. Instead of wasting time trying to answer questions that are pretty much buried maybe try written a play or a sonnet.