Last week I learned how to find a vertex, the x intercepts, y intercetps, the domain and range, the axis of symmetry, minimum or the maximum and if the parabola opens up or down. By using the formula y=a(x-p)2
With this formula I am able to find the vertex with the p+q values. The “a” tells me if the parabola compresses or stretches and the (x-p)2 tells me the horizontal translation. The formula at the top is in standard form which is the easiest to use.
And with the standard form formula you can also use algebra to solve a missing variable so that your equation will be inm that form. In the example below I will show you how to find all of the characteristics of the following equations.
Here is my example and the equation is positive so my parabola will be opening up and if my equation was negative then it will be opening down. The a also tells me if the parabola opens up or down so the formula is easy to understand and use to find all of the characteristics. I also used desmos to see the y int which was 13. Desmos has been very helpful to me because then I can see how the parabola looks like and know the x and y intercepts. The standard form also tells me all of the information and their is enough to graph a lot of points. Remember when you are graphing a parabola make sure to have a lot of points because its a curve and not a straight line and if you are stuck make a table of values and it will make it easier to graph. That is what I learned in class last week and can’t wait to learn more about parabolas.
This week I learned how to solve quadratic equations using the quadratic formula. The first step will have to be make sure your equation is equal to zero. In the example I have provided it is also equal to zero so all I need to do is substitute the values. Make sure to simplify the equation to get an answer. Some quadratic equations can have 2 solutions. In this case there are 2 solutions and some can have one solution. That is what I learned in math last week.
How did the discovery of DNA prove that Darwin’s theory of evolution was correct and how does it change the way we view evolution today and into the future?
Darwin didn’t have any evidence to prove his theory of evolution. His theory explained that all animals come from the same prehistoric animals, which were fish. Over the time, all animals adapted and mutated to create new species that can survive in the new environments that they are introduced to. Humans have evolved from fish, to apes and then to humans. This happened so that we could adapt to our environments. This was part of his theory as well, where he suggested that humans and chimps are relatives, which means that they are both descendants of the same ancestor. That ancestor would be a fish that once existed in the oceans. At the time, he had no hundred percent evidence since science wasn’t as advanced as it is now, but now we have the ability to analyse DNA, we know that Darwin’s theory was correct. Scientists were able to study ape DNA and compare it to human DNA. They found very close similarities in our genes, proving Darwin’s theory that humans and chimps are related. We also found that that humans and apes share 99% of the same genes. Darwin theorized that all animals on the Earth are descendants from fish. This couldn’t have been proven until modern day scientists found Tiktaalik, a prehistoric animal that had a transitional form with a fish body and the same bone structure found in all four-legged animals. This animal proved that his theory was correct because we can see from Tiktaalik how these species moved from the ocean onto land.
This week I learned how to multiply and divide radicals using simple steps. When you divide radicals if the denominator has a square root then you have to rationalize the denominator which means that I multiply the bottom with the top and then I use the distributive property or foil to get like terms and then I collect them and get my answer. For some other dividing problems you have to use a conjugate which means that I multiply the radical at the bottom by the same one except I need to have different signs, if the expression is positive then you have to multiply it by the same numbers but instead of the plus it has to be a minus. Because then it will create one zero pair and you get the expression that you need to have at the bottom. After you get that expression you just multiply it by the top and then you get your denominator that has no radical and its simplified. In my example I used the conjugate one so their is a visual to show how you solve those expressions. And if the bottom square root can be simplified to a simpler radical then you should change it so then you can work with easy radicals. I worked smarter than harder and that ugly radical becomes an easy one.
What I learned this week is how to write an entire radical from a mixed radical. The first thing you do is look at the square root number or cube root. Than the number that is in front you multiply it by your perfect square and after it is done you have to multiply the number that is inside of the square root by your first number squared. I found it easier to calculate it when its in a fraction cause you just square the number on the top and what is done at the top must be done as well at the bottom. Then you multiply that fraction by the one in the square root. That is how you write an entire radical from a mixed radical. Here is the example that I did from the workbook and since you can’t have negatives inside a square root you leave it on the outside, and that is what I shown in my answer. Also don’t forget to simplify the fraction if it is possible.
In class last week we learned how to calculate geometric sequences using a specific formula and you know that it is a geometric sequence if it has a common ratio and since the equation gave me my common ratio it made it easier to calculate. But some equations the r is unknown and to solve it you have to isolate the variable and then use the ratio number you get and substitute into your formula.
In this geometric sequence I had to determine the S5 by using the tn formula and get the answer. After using the formula I substituted the variables with the numbers in the geometric sequence and then I used my scientific calculator and plugged in the numbers that are in the brackets and then when I got my answer of -968 I had to divide it by a positive 2 since 3-1= +2. Then since I divided a negative with a positive my answer had to become negative due to the exponent rule. It was challenging and confusing at first but then when I worked through more problems I understood how to properly use the formula and what to plug into my calculator to get the right answer. Which now made it easy for me to calculate. The skill checks also very helped me understand how to show my work the right way instead of just messing up in the calculator and getting the wrong answer. Showing my work really helped me because if I messed up on a step then I can no problem go back and check and find out what I did wrong instead of guessing how to get that number.
Ms Burton I am sorry but my blog post didn’t properly post on Friday because shaw turned off my wifi and I had no idea until today in the morning when I decided to check.
Sugar gliders or their scientific name which is Petaurus breviceps. They are an omnivorous species of possum that can glide through the air. They are also marsupials which means that they carry their babies in a pouch. These species belong in the kingdom mammalia just like us humans. These creatures are found in trees and rarely touch the ground. Their membrane or the flaps on each side act like wings which allows them to glide. They are also called sugar gliders because they love the sweet nectar from fruits. So this creature belongs in the mammalia kingdom.
Tropical pitcher plants the scientific name of this plant is called nepenthes. They are a type of plant that belong in the plantae kingdom. They are called pitcher plants because they are a carnivorous plant that have cupped leaves that are filled with liquid that attracts flies and other insects to drink its nectar. The edge of the pitcher plant is slippery which causes whatever is on it to fall in and the plant eats it. The plant belongs in the plantae kingdom because it is an organism that absorbs water and other substances through its roots, and gets energy from photosynthesis.
common d= 5