Notes from Mrs. Caso
This project will demonstrate how parabolas and quadratic equations are seen and used in the real world. It will be split in two different applications. Everything you will need is listed at the left.
Lesson Plan
First we're going to look at how the water stream from a typical drinking water fountain forms a parabola. Then we are going to create the quadratic model for the picture of one water fountain. This is not going to be an easy task, but it can be done. You will plot the parabola between two x values: the minimum and the maximum. I want you to use 66 for the minimum and 420 for the maximum. Your goal for this part of the project is to use the formula f(x) = ax^{2} + bx + c to find the best model for the parabolic curve. Follow the
directions on the screen to test your choices for a, b, & c.
When you have found a curve that fits the water flow, show the
teacher and print the screen that shows the graphed curve. Then
close that window and print the screen showing your equation.
Use this simulator to see what happens when you change the a, b, and c in the equation (SIMULATOR) |
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You can go to
HowStuffWorks
online and it will explain how "Pendulum Clocks" work. | ||
The length of the pendulum regulates the timing of the clock.
Since the leaf acts as the weight on a pendulum, its distance
from the top of the pendulum pivot determines the speed at which
it swings. So, how far up or down do I have to move the leaf if
the clock is running 15 minutes fast each day? Our goal is to study the relationship between the length of a pendulum and the speed at which it swings. To do this, we are going to experiment with a virtual pendulum and collect data for the time it takes to swing 10 times at different lengths. Then we are going to plot our data on a scatter plot and fit a quadratic curve to the data. We'll use a computer to do the graphing and curve fitting. Then we'll try to answer the question above for Bonus Points. Okay, let's get started.
When done, go to the Quadratic Regression Applet.
On the back of the lab sheet, answer the following questions:
When you have answered the questions, staple your Pendulum Lab Sheet to the back of the Graph Sheet (graph showing on top) and turn it in. Answer the Bonus Points question on another piece of paper and turn that in within one week. (10 Points Possible) |