March 2018 archive

Week 7-Using the Discriminant

While solving quadratic equations, it’s useful to take a look at the discriminant.

The discriminant is area under the square root in the quadratic formula:

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if you have a quadratic equation (equation equal to zero with 3 distinct parts), you can use the quadratic formula to solve. Depending on the answer, we can figure out whether the equation will have 1,2 or 0 solutions.

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Let’s find the discriminant of the equation: x^2-3x+6=0

In a quadratic equation, the parent would be ax^2+bx+c

following the parent, in our equation, a=1, b=-3, and c=6

using this information we can plug in the numbers to our equation to find the discriminant.

If b^2-4ac is our equation, we just put our numbers we found in the spots of the letters, and simplify.

b^2-4ac

 

-3^2-4(1)(6)

 

9-4(6)

 

9-24

 

-15

 

using this we know that since the discriminant is -15, the original quadratic equation does not have any solutions, and using the quadratic formula would not work.

Week 6 – Solving Quadratic Equations Using Factoring

This week we learned how to solve a quadratic equation using factoring.

In order to solve the equation the zero product law must be used.

a*b=0, so either a=0 or b=0.

both sides if the equals sign must be equal.

for example: 8(x+2)(x-7)=0

x+2=0

so x=-2

also, x-7=0

so x=7

a quadratic equation has two possible answers. If you plug either of them into the equation, it should work.

8(x+2)(x-7)=0

x=-2

8(-2+2)(-2-7)=0

8(0)(-9)=0

8(0)=0

0=0

to solve any quadratic equation, the product must be 0. The equation cannot work without it.

Why feminism still matters to young people

Link to Article: http://theconversation.com/why-feminism-still-matters-to-young-people-91299

Feminism is the advocacy of women’s rights on the basis of the equality of sexes. Not that women are superior than men, but that we want to be treated equally in every sense. Some people still find it difficult to grasp the idea of an equal world. I personally am an avid supporter of this and choose to educate myself on how to be the best, and most insightful into this subject as possible. The article centers around how young people, especially young women, are using feminism. The #MeToo campaign is an example of how women are standing up and speaking out against abuse and harassment. The author is very descriptive and fact-oriented in a way that is both clarifying and educational.

Week 5-Factoring Polynomials

When factoring polynomials, we can use a system:

Common?

Difference of squares (2 terms)

Pattern (x^2 x #) (3 terms)

Easy 1x^2

Ugly ax^2

or for an easy jingle, Can Divers Pee Easily Underwater.

using these steps we can factor each type of polynomial to its simplest form.

for example:

3y(y+2) – 9(y+2)

because this polynomial has a common factor, y+2, we can substitute it for an unknown variable such as “a”

3ya – 9a

doesn’t that look better?

now we can use the to find the difference of squares because there’s 2 terms. If there are more than two terms you can skip the and go right to P.

3a is common on both terms so we simplify polynomial to

3a(y-3)

now we substitute our y+2 back for “a”.

3(y+2)(y-3)

and you’re done! this polynomial cannot be simplified farther.

For a polynomial with 3 terms, you will not use the D, but skip right to P depending on whether you have 1x^2 or ax^2 will decide if you use the E or the U.