During this project we learned about the vertex form of the quadratic equation and the different affects H, K, and A have on the way your parabola will turn out. Your A value is important because it will tell you if your parabola will be wide or narrow or if it will concave up or down. Your K value is important because it gives you the y-coordinate of the vertex on your parabola. And lastly your H value is important because it tells you the x-coordinate of the vertex on your parabola.
The quadratic equation in vertex form is Y= A(X-H)^2=K Worksheet #8 (pictured on the right) was the worksheet that gave me the most practice with vertex form. This worksheet is called "Using Vertex Form". In this worksheet we practiced looking at different parabolas and writing the equation of the parabolas we saw in vertex form. After practicing with this worksheet I understood this concept much better. |
There are two other forms of a quadratic equation besides vertex form they are standard form and factored form. The standard form of this equation is:
Ax^2+Bx=C The advantages of writing the quadratic equation in standard form are that it gives you the y-intercept which is c, and this equation is probably the most organized one out of the three. The factored form of the equation is: A(X-P)(X-Q)=Y The way I found that was I used the Habit of a Mathematician, look for patterns. The advantage of using this form of the equation is that it gives you the x-intercept. The two forms will produce the exact same porabla as you can see in the picture I inserted. I used the habit of a mathematician called be confident patient and persistent in order to learn these equations and be able to draw the parabolas from them. |
Kinematics
We used kinematics in this project by doing the worksheet called Victory Celebration. This problem is basically about High Tech High watching fireworks for a celebration. The fireworks are launched from a tower that is 160 ft tall. We were supposed to sketch the situation and write a clear statement of the questions students want to answer. This worksheet was the main problem in this project. This worksheet was helpful for us because it showed us that applying quadratics to kinematic problems it is very beneficial to problems like this. Geometry For this section there were a lot of worksheets and examples having to do with geometry. The worksheet that helped me the most is called a corral variation. This worksheet talks about a farmer that raises cattle that wants to build a pen for them. He uses an existing fence as one of the sides of the pen. For the remaining three sides he uses 500 ft of fencing. In this problem we were told to choose three possibilities for the dimensions of the rectangular pen. Then find the area of those pens. This worksheet shows the things that are similar between quadratics and geometry. It also shows how quadratics can help you with geometry. Economics In this problem there is a Acme Trading Company and they have a thousand widgets. The company knows that if they raise the prices, the lower the amount of widgets they will sell. I used the equation 1000-5d widgets, d=dollars. this worksheet really helped me understand how economics and quadratics can be used to help problems become more understandable. The problem was asking us to find a price per widget and how many widgets the company will sell at that price. |