Introduction:
This project was started when we got a worksheet of launching a rocket from a tower 60 feet high then it had a certain amount of acceleration. For this worksheet we had to find out how long it would take to the max height and from that point to the ground. Good thing about this problem was that the numbers were not too complex this is using the habit of a mathematician which is starting small. The kinematic equation was h(t)=-16+^2+92+160. This was in y=ax^2+bx+c.
Also this unit was about quadratic equations and how we can solving them. Once we learn a bit more about quadratic and Dr.Drew gave us a website for a online graph equation so we can see how it would look like on there. After a while we started getting worksheet and learning step by step what each quadratic equation would be. I was surprised by how many different “forms” there is.
II. Exploring the Vertex Form of the Quadratic Equation:
Vertex from is one of many forms of quadratic equations. The vertex form is y=a (x-h)^2+k. The h and k is how you figure out the parabola. This was the first form of quadratic that Dr.Drew introduced us to. We were introduced to demos which is an online graphing calculator and on this website we were first looking for patterns. A habit of a mathematical that was being used in this was looking for patterns. This worksheet was helpful because if not we would have to find out two x intercepts. Sometimes, there is not even the x intercept to find and it's kind a waste of time. Without this formula, it would require a lot of trial and error and plugging in numbers.
The formula that is being used in the first worksheet that I have is y+ax^2. After a while on being a demos and see how it works. I had a visual of what the patterns that Dr.Drew was talking about to look for. At first I had a hard time seeing the patterns but at time went by I asked my classmates if they can help me. I started see an equation and are if the parabola would conceived up or down, and where the x intercept would cross. With the equation gave the first step was to figure out a. What was nice about this equation was that it also told you how wide the parabola could be. The smaller a was meant the wider the parabola is. It's direct cause and effect. In order for the parabola to concave down it needs to be negative.
Once we got the hang of that, then we moved onto our next worksheet which is the picture above. For this worksheet we were then trying to figure out k. This was now adding on a new labor to our quadratic equation because it now didn't always start on (0,0). K is the determines where the parabola starts, it was the same equation but adding something on. The equation now is y=ax^2+k. K is the equal to the u coordinate on the acces. An example is if k 4, the point of the vertex is (0,4).
The next worksheet which is the picture above was to figure out how h effect the parabola. k, the vertex of the parabola changes when you change your k. Quadratic equation for this set is y=(x-h)^2. Which if you can tell is the opposite of k, h moved on the x axis. An example is if k was one of the coordination of the vertex would be (1,0). After this we now know how to do find out both the x and y coordinates of the vertex of quadratic function, we now know how to find a parabola. Dr.Drew then gave us a worksheet that put all of these individual skills together. It was confusing at first because then we had all of the quadratic equation together. But, a habit of a mathematical that I used for this was staying organized because if I was all over the place with it, it would confuse me more. For the worksheet I used the habit of a mathematical was taking apart the problem and then putting it back together.
III. Other Forms of the Quadratic Equation:
The picture that I have above standard form which one of the forms we learned in this unit. Standard form is y=ax+bx+c. Standard form has an advantage which is very useful to find the y intercept of the parabola which we figured out is always c.
The picture I have above is factored form. Factored form is y=a (x+p)(x+q). Factored form advantage that it has is that it shows you where the x intercept is. This form is not really my favorite because I don't really get it. For this form Dr.Drew tells us to F.O.I.L (first, outside, inside, last). Factored equation p and x are the x intercept.
IV. Step by Step Examples:
V. Solving Problems with Quadratic Equations:
Now that Dr.Drew has taught us everything around quadratics and can solve real world problems like for example the rocket problem which is how we started this until. After this I can find the coordination between velocity / time also the height/ time. By using kinematic, we can figure out anything projectile motion. Using geometry, we can figure out triangles and rectangles area problem. Using economics, we can figure out how people get their money. A worksheet that showed us a real world problem with quadratic was the widgets.
VI. Reflection:
Overall this until was hard because it was something new and a use a lot of memorization with the formulas and knowing how to use them correctly. If you did not use the formula correctly it could really mess up on your work and you need to start all over again and it will just get you more confused on what you're doing. It was really nice learning something new all those stuff because it's prepare us for next year math. I am so worried about the SAT because math is not my strongest subject and I'm really slow with understanding. I'm really worried about next because I know throughout the years math is going to get more hard and it's going to be more different and since I'm a slow person with maths I feel like I am going to get left behind. I know that for next year for sure I need to ask my teacher for help when it's not too late and I need to go to office hours because I didn't do that this year and I know if I did it would make me understand this math more and I wouldn't feel like I'm behind. I'm good with note taking but it just takes me a while to understand it so I feel like I need that one-on-one with my teacher to understand and comprehend the contact behind the math.
Habit of a mathematical:
Throughout this until I worked with my peers and I listen to them and see what they had to say. I seemed why and priced in the formulas. I stayed organized by keeping my worksheet. I was systematic by I had a goal for a day or week and I'll finish them. I looked for patterns.
Overall this until was hard because it was something new and a use a lot of memorization with the formulas and knowing how to use them correctly. If you did not use the formula correctly it could really mess up on your work and you need to start all over again and it will just get you more confused on what you're doing. It was really nice learning something new all those stuff because it's prepare us for next year math. I am so worried about the SAT because math is not my strongest subject and I'm really slow with understanding. I'm really worried about next because I know throughout the years math is going to get more hard and it's going to be more different and since I'm a slow person with maths I feel like I am going to get left behind. I know that for next year for sure I need to ask my teacher for help when it's not too late and I need to go to office hours because I didn't do that this year and I know if I did it would make me understand this math more and I wouldn't feel like I'm behind. I'm good with note taking but it just takes me a while to understand it so I feel like I need that one-on-one with my teacher to understand and comprehend the contact behind the math.
Habit of a mathematical:
Throughout this until I worked with my peers and I listen to them and see what they had to say. I seemed why and priced in the formulas. I stayed organized by keeping my worksheet. I was systematic by I had a goal for a day or week and I'll finish them. I looked for patterns.