Introduction to Quadratics:
For most of the second semester, our class - Class D, have been mainly focusing and learning about quadratics and kinematics. So far we've reviewed and turned in 25 worksheets that we were given in class to help us improve our understanding in quadratics. It was April when Dr. Drew had given everybody practice problems and in our first handout we mostly went over things like distance (d), velocity (v), and acceleration (a). For the past three months we have been mostly working on 3-4 worksheets that would be due every two weeks, usually depending on how challenging it was. After that, that was when Dr. Drew decided to change it up a little for handouts 4-6 and we started going over and learning about Parabolas. After we had finished and turned in the work sheets for Parabolas, Dr. Drew had introduced us to 'Vertex form'. In handouts 8-9, our job was to figure out where the vertex was, what was the equation, if it will concave up or down, and where it crosses the axis.
By the time we started to actually work on quadratics we were just barely starting handout 12, our jobs for this handout was to distribute the area by creating a large rectangle that is cut by lines parallel to its sides into four smaller rectangles. All we were really doing for this handout was using this area diagram for factoring numbers the given numbers and changing them to 'standard form' y=ax^2+bx+c. We worked on these until we got to handout 14 and for handout 15 we had to complete the square and even though I had a hard time trying to solve the problems, I got help from my classmates and was told that if you divided 'b' in the previously stated equation. From there your job is to square that number to get 'c'. The rest of the handouts go more into detail with quadratic equations and helping you practice in the meantime and we used Desmos.
Exploring The Vertex Form Of A Quadratic Equation:
For this part I am just going to talk about when our class was using an online graphing site called Desmos and this would help a lot with trying to visualize the size and the location of a parabola and finding the vertex. Because of Desmos we were able to graph the equations that we found and this helped us with trying to find out if we were correct or not and we were also able to see what each of the parameters of the equation do. Here's an example of one of them:
Ex. With it in 'vertex form' we saw what each part did and it is y= a(x-h)^2+k by putting in the equation of y=ax^2 just by messing with the 'A' values. I learned a lot in class while working on some of the handouts and it helped me understand how to solve quadratic equation.
Info:
A = 'Area' and it affects whether the parabola concaves up or down, depending if it was a negative or a positive, and how wide it is because whenever the number for 'A' gets bigger, the parabola gets narrower.
H = 'Height' and it also represents what the X coordinate of the vertex is.
K = It represents what the Y value of the vertex is.
Standard Form: y=ax^2+bx+c
Vertex Form: y=a(x-h)^2+k
Factored Form: y=a(x-p)(x-q)
Vertex Parabola: v=(h,k)
Converting One Form To Another:
Handouts:
#14 - #17 #18 - #22
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