FFPC+Mathematical+Reflections,+p.70

Zareen K.  Thursday, February 12th, 2009 Block 8D: Advanced Math
 * Big Idea:** Quadratic Functions help us describe situations in the real world.
 * Essential Question:** How can I make a prediction using quadratic relationships.

// Investigation Four // One way is kicking a ball upwards and watching it go up and descend over a period of time. A second way is it can model business situations, for example when prices or stocks soar and/or decrease that can be graphed for businessman. This in fact, often appears in newspapers (in the business section.) Quadratic functions are often used to determine change in oil prices and Wall Street Stocks. The third way that I thought of finding the dimensions for the maximum area for a given perimeters. In a quadratic relationship table the second differences are constants and that is a way that you can tell the function //is// quadratic. The first pattern is that the quadratic function always produces a parabola. The difference is which direction the parabola faces. If the constant variable (a) is bellow zero that it is a regular parabola: it first goes up and then comes back down to the starting point. If however, the constant is above zero than it will be a reverse parabola and have the opposite pattern. If the equation has the x squared (x^2) value. The equation can come in two forms the first of these is factored form: (x+2)(x+2) The second form is expanded x^2+4x+4 ** Investigation Four ** // Summary // In this investigation I learned about the relationship between time and height and found similarities between quadratic relationships/functions.
 * Mathematical Reflection**
 * // 1. Quadratic functions can be used to model many real-world situations. Describe three situations for which quadratic functions are appropriate models. For each situation, give example of questions that quadratic representations help answer. //**
 * // 2. What patterns of change occur in tables of (x,y) values for quadratic functions? //**
 * // 3. What patterns of change occur in graphs of quadratic functions? //**
 * // 4. How can you recognize a quadratic function from its equation? //**