Quadratic Performance Task

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Christy Knudsen

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Jan 4, 2014, 3:41:52 PM1/4/14
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Math Team, I need your research help! 

One of our credits in Alg2 is on quadratic equations and modeling quadratic data. I know there are many ways that quadratics show up in life. I have lots of ideas for interesting subjects I could, but I am having a very hard time finding actual data that students could work with to solve a task. Below is a list of some of the subjects I thought of. Does anyone have any resources that I could find data to use? 

Military air training for dropping bombs (inspired by my trip to the Ocotillo Wells where there are targets and military practice bombs)

Evel Knivel jumping cars

Building suspension bridges

Water slide jump (inspired by this viral video http://www.youtube.com/watch?v=3wAjpMP5eyo and Mythbusters actually proved video fake)

Military cannon shooting


I know this topic is easily applicable to real life situations, but coming up with a good performance task and using GRASPS is challenging. So anything will help.

Thanx!
Christy

Sarah Soares

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Jan 6, 2014, 12:37:32 PM1/6/14
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Christy, I'm looking into this.  I will let you know if I find anything.

Steve Cates

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Jan 6, 2014, 5:49:04 PM1/6/14
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Aside from the path of a projectile there are several more examples of using quadratic equations to solve problems here's a few I've used in the past:

Areas of shapes with variable length sides.  Example a frame with 3" border would have an area of A=(x+6)(y+6) and if you related x is say twice y then you'd have a quadratic equation for the area A=(x+6)(x/2 +6)


Approximating any curve based on three points.

Trianglular numbers 1, 3, 6, 10, 15 ...  governed by (n)(n+1)/2 

My favorite example from structural engineering is Moment in a beam.  Example a simple concrete beam with steel at the bottom has the bending capacity of M = As fy (d - As fy/(0.85 f'c b))  Typically you want to solve for the Area of steel As.  Rearranging that equation plugging in values for the Moment (M), yield strength of the steel (fy), depth of the beam (d), width of the beam (b), and concrete compressive strenght (f'c), you would have a nice little quadratic with Area of steel (As) as your unknown.  I doubt it could factor be factored though so the student has to resort to the quadratic formula ;)

Also, anytime you need the area under a line, calculus tells us that it's a quadratic so that opens up almost any topic that you can think up.  I guess you could go the other way and say the instantaneous slope of a cubic is a quadratic too but that seems a little far a field from high school algebra :)

Sarah Soares

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Jan 7, 2014, 12:49:19 PM1/7/14
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I haven't found anything particularly good so far.  

But speaking of quadratic formula...

Timothy Kim

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Feb 9, 2014, 12:06:08 PM2/9/14
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Hey, Christy, I'm not sure if you can still use this but I've been a little out of commission lately with work and life but I finally have some breather room to look at some CC stuff being posted.

1. I found this webpage on some useful parabolic function problems that might spark some creativity.
Not sure if it has the specific data you were looking for but here it is:

2. Here is a youtube video for a practical project on making a parabolic reflector/mirror using old satellite TV dishes if you can find one in a salvage yard.
You can get a pretty cool focused heat source using the focal point if you can get your hands on some pretty shiny reflective material:

3. Here is one on parabolic art:

4. You can also buy a pretty cool 3-D parabolic illusion/magic hologram gadget container that uses the focal points of two parabolic surfaces to create a hologram of a small object reflecting a small penny sitting on the bottom of a parabolic surface magically on to the opening of a parabolic lid right where the focal point is located. And it is only about $10. I think Karl should get a purchase order to have one for each cohort member during our next cohort meeting.
:)

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