weaks5_7

Weaks Period 5

__**The Mathematicians**__- Jaren Butler - Math cruncher Edgar Santiago - The Facilitator Donovan - Recorder

Follow the directions on the Vertical Motion page, to complete each of the sections below.
This is the right equation because the question asks how much time it will take a snake to escape a hawk that is swooping down at it, so its a thrown object because its propelling itself down.
 * __The Word Problem__:** A red-tailed hawk dives toward a snake. When the hawk is at a height of 200 feet, the snake sees the hawk, which is diving at 105 feet per second. Estimate to the nearest tenth of a second the time the snake has to  escape. [[image:red-tailed-hawk-flying.jpg width="275" height="191"]]

h= the height of the object at any given point in time. t= time of the object in motion(seconds). = The initial height of the hawk. v= the initial velocity in feet per second.

Standard Form of our equation.


 * __The Parabola:__** Use what you know about parabolas to predict the shape of the graph. What will it look like, and how do you know?

a= -16 b= -105 c= 200.

"a" will affect the graph because if its positive, the parabola goes upward. If its negative, the parabola will go downward. Since "a" is -16, the parabola will be narrow, and the parabola will go downward. "c" is y-intercept of the graph, it also determines where the vertex will be located. Our graph will cross the y axis at the point 200 of the y axis. Discriminant: The formula to find the discriminant is... The discriminant shows how many "root's" there will be on the graph. Our graph contains 2 "roots."

Axis of Symmetry: -3.2, this is where our graph can be cut in half and have the same symmetry. And it is also the "x" coordinate to our vertex. Vertex: All we did is plug in our AoS into our standard form equation, and simplified to find the "y" coordinate of the vertex. Graph=
 * __The Math__:**

The best way to solve for "x" is to find th axis of symmetry, which is. This is the method I used because it gave the "x" coordinate on the graph.

1.The solution means that the snake will have about 1.5 seconds to escape from the diving hawk. 2.The vertex represents nothing because there is no such thing as negative seconds. 3.The y intercept represents the height it started from because as the parabola goes downward, it intersects 200, where the hawk started diving at, and the line comes down and intersects the x axis at 1.5, which in seconds is the time the snake has to escape before the hawk gets it. 4.I believe the roots represent how long the hawk is in the air before, and the time it takes for it to hit the ground 5. So the hawk was in the air for 8.1 seconds to locate the object, and it took 1.5 seconds to swoop down in the air and hit the ground.
 * __The Solution and The Meaning__:**

__Jaren:__ What I found difficult about this project was doing the math and graphing the function because before I didn't understand anything about vertical motion or how to solve a problem like this. To make the project run smoother I would of had to understand how vertical motion works and how to solve it. This project helped me understand vertical motion because it's just like how to solve regular quadratic equations, you put it in standard form and solve for the axis of symmetry and vertex, then use the quadratic formula to find the roots and finally just graph the rest. It felt different to do the work like a teacher because you have to go deeper into a problem like you're teaching it to someone. __Donovan:__ What I found most difficult to do was the math because we worked on it for a couple of days and found the answer later. What I would do differently next time is to divide the work between each other so we could finish it in time. Yes it helped me because before I couldn't understand it but now I can solve quadratic equations. It was a very good experience to do this project and I would do this again because we all had fun doing this. __Edgar:__ I found all the calculations and graphing very difficult because I didn't really know how to do this kind of stuff very well. Throughout the whole time of working, we had to ask for help because we got stuck on the problem many times! What I would do differently is I would make every person do different jobs, so my group could multi task. This project helped me a lot because when the teacher and Jeremy explained it to us, it made more sense. When we did part 3, I felt like we were teaching an alien.
 * __Reflection__:** How did it feel to do the work and pretend to be the teacher? Do you think you understand the material more, now? Why or why not?