Introduction
This investigation is about a steel ball that was launched and had its heights recorded with the corresponding times. The data was then documented as a table and as a chart. The assignment for this investigation was to find the equations that defined the positioning of the ball, the velocities of the ball, and the acceleration of the ball. To find these functions, I used the data and chart to make transformations to the initial equation, y = x^2.
The Academic Skills and Objectives That I Used Were:
- Add, subtract, multiply and simplify polynomials and rational expressions
- Solve polynomial equations and equations involving rational expressions
- Verbal descriptions into mathematical expressions
- Know and use a definition of a function to decide if a given relation is a function
- Perform algebraic operations (including compositions) on functions and apply transformations(translations, reflections and rescaling)
- Know and apply the definition and geometric interpretation of the difference quotient
- Simplify difference quotients and interpret them as rates of change and slopes of secant lines
- Translate written description of a real world problem into a mathematical model
- Assign independent and dependent variables Be able to find minimum or maximum value in a real world problem
- Explain how the rates of change of functions in different families (ex. Linear functions and quadratics) differ, referring to graphical representations
- Apply quadratic functions and their graphs in context of motion under gravity and simple optimization problems
- Find a quadratic function to model a given data set or situation
Justification
These three functions each correspond to different characteristics of the steel ball's motion. The first function, "p", defines the position of the ball (y) at a given time (x). The "v" function defines the velocity of the ball (y) at a given time (x). And the "a" function defines the acceleration of the ball. These three functions each correspond with each other. The velocity function was discovered through synthesizing the positioning function. And the acceleration function was discovered by synthesizing the velocity function.
I put this investigation in my portfolio because I understand it and can explain it well. Also it shows a lot of the skills I learned about graphing and transforming and constructing functions.
I put this investigation in my portfolio because I understand it and can explain it well. Also it shows a lot of the skills I learned about graphing and transforming and constructing functions.
shot_in_the_dark_worksheet.docx | |
File Size: | 21 kb |
File Type: | docx |