Digital Portfolio Update
IntroductionTo start this project off we got a worksheet called "Distance, Velocity and Acceleration. For this worksheet we worked on finding distance, velocity and acceleration in graphs. We had to figure out what the graph was representing. We then did a paper called "Victory Celebration" where we had to use what we learned from the first worksheet to sketch and figure out the velocity, distance and acceleration. After that we moved on to parabolas. For these papers we had to find equations for the parabola and graph them using Desmos. The next worksheet after this we focused on vertex form but specifically vertex from for parabolas. We found out that general equation for it is y= a(x-h)^2+k. A few of the worksheets had us try to completing squares to change an equation from vertex to standard form. We got one worksheet that was called "How Much Can They Drink" and it focused on volume, more specifically the volume of a drinking trough. When we were getting close to the end we did a packet where we focused more on Pythagorean theorem. We used the equation a^2+b^2=c^2. For this problem we had to find x, which in this case was a missing side to a triangle.
(Examples of work on the below) Example of Pythagorean Theorem. Exploring the Vertex Form of the Quadratic EquationDuring these series of handouts we used an online graphing site called Demos that helped us graph the equations and see what they would look like. While we were on this site we got to explore how a, h and k affect the equation y=a(x-h)^2+k. After a while we learned what h, k and a do. H is the x coordinate, a decides whether the parabola concave up or down(Negative means it conclaves down and positive it conclaves up) and it also its changes how wide or slim it is, k is the y coordinate. (Example of work down below) Other Forms of the Quadratic EquationStandard form is ax^2 + bx + c = y. It is the most used form for the equation of a parabola. It is more organized than other equations and it also gives us the y-intercept value which is c. Factored form is a(x - f )(x - r) = y and it is useful because it gives us the x-intercepts. Example: If the equation was y =3(x-5)(x-2) then the x intercept coordinate must have a y value that is zero because if we rewrite it as 0=3(x-5)(x-2) then we know that the parenthesis have to equal zero so that the equation actually work, That being said x has to be 5 and 2. (Example of parabola below. Converting between FormsWe solved these problems by using equations and other things like and area model. An are model is a square that is divided equally into four sections and you use it to help you plug in your information. It is a good visual to have and it helps a lot.The slide show to the right shows step by step how to convert between vertex to standard, standard to vertex, factored to standard and standard to factored without an area model. The images below show me using an area model to help me go from vertex form to standard and standard form to vertex. |
Reflection |
During this whole project I learned a lot about quadratics. Even though we got a lot of work for this project I did turn them in on time and kept them all together. I would have to say that my biggest takeaway from this is that team work and collaborating is essential. Me and my table members helped each other a lot and I am very happy about it. I think this project should not have been so as rushed as it was because we were doing like a paper a day and they started to pile. It was a little overwhelming because there was a lot of papers but that didn't stop me and my table from getting at least two papers done a day. I can easily say that I used each one of the Habits of a Mathematician because of how much their was to this project. Each one of them played a role in this project and was very important for me to use so I could succeed. My goal for 11th grade is to keep collaborating with my table members. I would like to continue to study for the SAT because I am not sure if I'm prepared quite yet.
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