Week 12 – graphing absolute value linear equations

Posted on May 6, 2018 by colinp2015

This week in Math, we learned how to graph and interpret graphs of absolute value equations. Since absolute value generally means that a number will always be expressed as a positive value, then the output values of our graph will always be positive. Below is what the graph of the parent function looks like.

Image result for absolute value linear equations

As you can see, the y value will always be greater than or equal to zero.

To express the equation without absolute value symbols we use what is called piecewise notation.

For the parent function, it would be:

$y=x, x\geq0$ ,

$y=-(x), x<0$

The line on the left is simply the opposite (negative) version of the linear parent function y=x.

Week 11 – solving inequalities

Posted on April 29, 2018 by colinp2015

This week in Math, we learned how to solve quadratic inequalities.

Ex. $x^2+2x<8$

Get the 0 on one side: $x^2+2x-8<0$

If we think of this inequality as a parabola on a graph, we would have to find the zeros to determine when the parabola is negative (because it cannot be bigger than zero).

Factor: (x+4)(x-2)<0

zeros: -4, 2

Because we know that the parabola is opening up and that there are two solutions, our answer would have to be when the parabola is in the negative part of the graph.

Therefore,

-4<x<2

Week 9 – Factored form of quadratic functions

Posted on April 14, 2018 by colinp2015

This week in Math we learned how to interperet graphs of quadratic functions in the form a(x-x1)(x-x2).

Ex. We can convert the general form of $y=2x^2+6x+4$ into factored form.

y=2(x+2)(x+1)

We can now find the x intercepts by utilizing the zero product law.

0=2(x+2)(x+1)

x=-2,-1

If we now plot these points on the graph, we can determine the axis of symmetry by figuring out the x value in the middle of these points, in this case, the AOS would be x=-1.5. We now also have the first x value of our vertex. We can then plug in this x value into our equation to solve for y value of the vertex.

y=2(-1.5+2)(-1.5+1)

y=-0.5

Vertex:(-1.5,-0.5)

Bloglog – Illegal exotic pet exports

Posted on April 13, 2018 by colinp2015

https://www.nytimes.com/2018/04/09/science/illegal-wildlife-reptiles-amphibians.html

This article talks about the exotic pet industry and how it is an industry that is corrupt with a lot of illegal activity. The author uses a headline that suggests that reptiles sold in pet stores are often either bread illegally or taken from the wild. The author exemplifies that a lot of the illegal activity that goes on in this industry occurs in third world countries, where a lot of these animals live, and because of that the law enforcement is unable to shut down these illegal operations. This article interested me because it makes you wonder about the source of things. When you see clothes in the shelf of a store you wonder if it was made abroad, in an illegal sweatshop or if it was made legally. This article illustrates that it is important that you know where all your purchases come from because in the this case especially we are talking about living creatures who have probably had a rough life.

week 8 – Parabolas

Posted on April 8, 2018 by colinp2015

This week in math we learned how to interpret information by looking at a parabola of a quadratic function.

Ex. $2x^2+6x+4$

vertex: (-1.5, -0.5)

axis of symmetry: x=-1.5

minimum value

x intercepts= (-2,0)(-1,0)

y intercept= (0,4)

domain: x E R

range: $y\geq-0.5$

Blog Log – Fake news

Posted on March 12, 2018 by colinp2015

https://www.nytimes.com/2018/03/08/technology/twitter-fake-news-research.html

This article was very interesting for me because it was about an MIT study about human behaviour regarding fake news and real news and how fake news will spread quicker on social media than real news. The author of the article illustrates that fake news tends to spread more because it the news is falsified in order for it to become more interesting. Of course when an article is more interesting people will share it more on social media. I think most of us, including myself, have come across a piece of fake news on the internet and were enticed to learn more contrary to real news which contains a more boring tone. This study exemplifies human nature and the way we, as humans, process information we see online. The article also mentions that it is very important know the source of news story and think for yourself if what you are reading is reliable and believable. This type of human behaviour is applicable not only to news; for me, I tend to do this for anything I see online. If it looks interesting, I’ll learn more about it, and if it doesn’t look interesting I will not learn more.

Week 6 – Solving quadratic equations by factoring

Posted on March 11, 2018 by colinp2015

When you have the equation $ax^2+bx+c=0$ you can solve for x by factoring this equation

Ex. $x^2+8x=-15$

$=x^2+8x+15=0$

Now that we have the factorable equation into the form we want, we are now able to factor it into two binomials so that when we multiply them it equals ar equation.

$(x+3)(x+5)=0$

We can see now that x has two possible answers because when one of the binomials equals zero than we still have 0 on the other side since n*0=0. So, we know that our two possible values for x are -3 and -5 because when we add them back into the equation, we get 0.

Week 5 – factoring polynomials

Posted on March 4, 2018 by colinp2015

This week in Math, we learned how to factor polynomials.

Ex. $8x^2-32$

If we want to factor this, we must remove a common factor from each term. In this case, a common factor is 8.

$8(x^2-4)$

This is factored, but it is not factored all the way because we can see that there is a difference of squares in the brackets. To simplify this, we must multiply conjugates.