This week in pre calc 11 we started chapter 4, and the first thing we learned was properties of quadratic functions. Now it’s important that before we start listing off the properties of each of these quadratic functions, that we know 100% that this is a quadratic equation. How can we tell if a function is linear, quadratic, or neither. In this blogpost I’m going to show you how you can tell the difference between a quadratic function and a linear function by looking at the table of values for any type of function.
Linear – look at the first differences, if they are equal to each other than it is a linear function.
Quadratic – Look at the second differences, if they are equal to each other than it is a quadratic function.
Neither – Than it just simply doesn’t follow any of the rules from above and is not a linear or quadratic function.
Ok so lets begin, suppose we have this table given to us:
The first step is to find the first difference, how you do this is to find how much space is between each of the #s.
As you can see, the first differences are equal to each other therefor this is a linear function.
Let’s look at another example:
Follow the same steps as you did for the function above:
As you can see, the first differences aren’t equal to each other so now we have to find the second differences:
The second differences are equal! Therefor this is a quadratic function.
Lets look at one last example:
First – find the first differences:
The first differences aren’t equal so we move on to step 2 – finding the second differences:
For this example both the first and second differences are not equal therefor this is neither a quadratic or linear function.
This week in pre – calc 11 we learned chapter 2.6 – solving equations algebraically. One thing that stood out to me was learning how to rationalize the denominator to solve an equation that looks like this one:
The first step is to multiply the “rationalize” it. The multiplies with everything and cancels out the on the bottom of the equation.
The next step would be to further simplify but as we can see we no longer can simply this equation further, so we leave it like this
Here is an example of an equation which also requires to be rationialized, take a couple seconds and try to solve this using what you know about rationalization:
Below is the answer and me solving this equation using rationalization:
This week in class we started unit 2 called Radical Operations and Equations , and the first thing we discussed was how to simplify radicals. We went from an entire radical to a mixed which we already knew how to do from the previous unit so I felt pretty good about it, and then we added a variable with an exponent to the radical like When I took a look at this I understood how to turn it into a mixed radical except I had no idea what to do with the variable with the exponent. So here’s the way that I deal with that variable and some tips that will make it easier for you to remember how to deal with that variable when it pops up in more complicated questions.
1st – Find the prime factorization, when you have a variable with an exponent you also find its prime factorization. * Realize that is a squared root therefor you are looking for pairs when finding the prime factorization. What I do right away is highlight my pairs right away so that way I won’t miss them.
2nd – once the prime factorization is found you will take the pairs and square root them and put them on the left side of the radical symbol taking it “out” or “removing it from the radicand area and then taking whats not highlighted multiplying them together and putting it on the inside of the radical symbol making it the radicand.
Have you ever wondered about how large the universe is? Well I guess you can say very. We have about 100 billion stars in the Milky Way galaxy, which is only one of about 3000,000,000,000 galaxies in the what we call “known Universe.” Which in other words is the part of the universe we have discovered. So with that being said, how is it logically possible that we are alone.There are many different theories from all over the world that prove life does exist and also arguments about why life doesn’t exist anywhere else within the universe except on earth. Below I have five of the most popular and well known theories that were brought up through time about whether life exists anywhere else within the universe.
Picture of the universe
How all of these theories started was when a man named Enrico Fermi asked himself this question, ” Given the scope of our universe, why haven’t we found intelligent extraterrestrial life yet, or why haven’t they found us?” since then many scientists all over the world have started researching and proposing many theories, within the century.
The first theory is called the Great Filter which is based on basic common sense that aliens must exist. As of now we haven’t made contact with any other life source within the universe, so this theory states that there could be a barrier that doesn’t allow life from interstellar travel. Which is a term used for travel between stars or planetary systems. This barrier is called the “Great Filter,” and it is a force or occasion that takes place to prevent a civilization from getting to the prior point of interstellar travel or communication. However there are two different reasons that these theories have proposed is why we haven’t been able to contact life. The first one being, societies kill themselves off before reaching an advanced state to explore the stars, or that interstellar travel is just not possible on a technological scale.
The second theory is called, “Do not disturb the aliens”. This theory was developed by researchers at Oxford’s future of Humanity Institute and the Astronomical Observatory of Belgrade. What they have come up with is that alien civilizations do exist but that they are inactive. What this means is that they are simply hibernating until the conditions in their environment allows them to build their own society.
The next theory persists that life needs a certain environmental condition to develop, this is called the “Gaian Bottleneck”. Their argument is that in order for life to be habitable, it has to first be inhabited. This is because organisms change the concentration of greenhouse gases in the atmosphere. They believe this is what happened on Earth.
This next one is more about how we are going to contact life and how we have been trying to do so since we have been asking this question. For the past 80 years we have been using the Allen Telescope Array to listen for signs of life, waiting to receive radio signals from any extraterrestrial life. although there are many arguments saying, what if extraterrestial life doesn’t operate on the same frequencies. So a man named Duncan Forgan proposed creating a galactic communications network. He wants to come up with a way to use the shadow that Earth creates when it passes in front of the Sun to send a message to whatever life exists within the universe. How he wants to address this message is by building powerful lasers that contain those encoded messages, which are sent out as we pass in front of the Sun.
Another argument is that we are being impatient. Which is basically stating that we have only been reaching out for alien life for about a century now. Evan Solomonides a researcher at Cornell University, suggests that it could take about 1, 500 years for us to hear from any extraterrestrials. He says,”We predict that under 1 percent of the galaxy has been reached thus far, and we do not anticipate to be reached until approximately half of the stars/planets have been reached.” In other words he is basically summarizing that we have found only one percent of the galaxy it will take a while to reach the rest and perhaps when we do we will run into life. He also says 1, 500 years isn’t a deadline it is just a point that marks the fact that we won’t be hearing anything before that time.
My opinion and sort of theory about all of this is that I think there is life out there somewhere within the universe. There may not be tiny little green men or “aliens” as we like to call them, but I do believe there is life existent on another planet within another solar system. Although looking back at all of the theories that I have researched it seems like we won’t be discovering whether there’s life out there within our lifetime. I don’t think we have reached the potential knowledge and technology that we need, in order to further take action on this matter. We haven’t even discovered all of the ocean yet let alone the whole universe. Although I’m certain that one day we will be capable of discovering life somewhere else whether thats a century away or a millennium away.
This week I didn’t understand how to get the answer for the following question because I didn’t know the steps that had to be taken in order to solve this question. After asking for help I understood what to do to answer this question correctly. Below are the steps I took in order to solve this question.
A challenge that my group faced during this video is that one of our group members was gone on a trip during the period of the video making and due date. There was many Wi-Fi and electricity shortages on her trip that she didn’t expect. This led her to not being able to get her tasks finished. Unfortunately, there was only 2 days left until the due date. Me and the other group member started coming up with solutions to this problem. First, we set a date to meet up at lunch. Then we divided the work up into parts. Writing the script and editing the video. communicating and talking about the situation really helped us get through this problem and get the project finished in time. Making this video was really fun, because we got to research about something we were interested in and let others know about it. Some useful tips about how to make an amazing video are not leaving it till the last minute, communicating and planning with your group, using different sources to research about your topic, and having fun! Overall, I’m very happy with the way our video turned out in the end. Even though we had a few bumps along the road, I was still able to communicate with my group and solve the problem.
Last week during science we went outside to the Oxbow pond located on the Port Coquitlam trail, to test the water quality and find different invertebrate samplings. Each group was given a compound to test out during our time in the pond. The next day we headed out to the Coquitlam river to find invertebrate samplings.
Water Quality: The compound that my group tested was nitrate, and the result that we got was 1.0 mg/L NO3. The overall water quality index value for the Oxbow pond is 82.24, and the water quality index value for the Coquitlam river is 89.43. These values tell us that the health of our pond is very good. This means that our pond is not harmful to any species around it, and is safe to be used from.
Invertebrates: The various kinds of invertebrates that my group found in the Oxbow pond is the Dobsonfly and a fish. None of the other groups got what we got in the Oxbow pond. In the Coquitlam river we unfortunately only got one invertebrate, called the stonefly. Only one other group got the same invertebrate as my group. The sampling results at the two different sites don’t really compare because they aren’t the same invertebrate. But both the pond and the river have living invertebrates in them.
Water Quality/ Invertebrates: The water quality in the Oxbow pond and the Coquitlam river is excellent, according to our overall water quality index values. This leads to a lot of invertebrates living In the water.
Reflection: Going outside and doing these activities really helped me understand water qualities and invertebrates a lot better. I really liked being able to experience what a scientist actually does on a daily basis. Working in groups also helped me because, I was learning and having fun with friends at the same time.
How might your digital footprint affect your future opportunities? Whenever you are using the internet you
have to be very careful, because that's how other people see you. Those people include future university or college deans of administrations, Bosses and other important people in your life. In order to get accepted into any university or college, or get hired for a job, it is very likely for them to check you digital footprint. Know that whatever you post
on your digital footprint has to be respectful and professional, because anyone has access to your digital footprint.
Describe at least three strategies that you can use to keep your digital footprint appropriate and safe.
Keeping your digital footprint appropriate and safe doesn’t mean that you should delete or not have social mediaF. It simply means that whatever you are going to tweet, post, comment, pin, or upload should be appropriate and safe. There are so many ways to help keep you in check. The first strategy is asking your self questions. Ask yourself, is this necessary? Would you want your mom seeing this? Is it useful? Is it respectful? By asking yourself these questions, you are making sure that whatever is going on your digital footprint is appropriate and safe. Another useful strategy is googling yourself. Googling yourself will show you what’s on your digital footprint and show you what everyone has access to. If you ever do find something that you don’t want on your digital footprint, simply delete or untag any unwanted stuff.
What information did you learn that you would pass on to other students? How would you go about telling them?
Your digital footprint starts from the day you were born. The social media and the internet is all around you. So you have to be very wise and careful using it, for it can affect you in the future. Using your social media and internet carefully is definitely worth it, because if you are ever looking for a good career when your older you have to have an appropriate and safe digital foot print. I can share my knowledge with other students by using the tag #ADL17footprint.