4.3+Putting+It+All+Together

Feb 12,2009 SM //Big Idea:// **Quadratic functions can help us describe situations in the real world.** //Essential Questions://How can I make a prediction using quadratic relationships? //Notes from class://  > equation has a linear pattern. //Problem 4.3// your tables showing first and second differences. y = 2x (x + 3), y = 3x - x^2, y = (x - 2) ^2, y = x^2 + 5x + 6 B. Consider the patterns of change in the y values and in the first and second differences for the four equations. In what ways are the patterns similar for the four equations? In what ways are they different?** B. In all the patterns the similarities are that we subtract the number itself. For example: if in the y-axis 36 is after 49 we do 36-49 and not 49-36. Another similarity is that in the second difference all the numbers turn out to be linear. The difference is that there are positive and negative numbers. //Problem 4.3 Follow up// and exponential functions you studied in other units. a. Make a table of (x,y) values for each equation below. Include columns for the first and second differences. y = x + 2, y = 2x, y = 2^x, y = x^2** patterns similar in the four tables? How are they reflected?** b. In these tables the similarities are that the numbers increase and decrease just and if it were shown in a graph it would look like a parabola. c. In the every equation there is a 2 and in every table there is a hint of 2 for example the first difference has all two's or if you had a third difference there would be all two's. Describe the graph of each equation in Problem 4.3 and question 1 above. Be sure to consider maximum or minimum points, x-intercepts, and lines of symmetry. Use a calculator to check your descriptions.** 2. All the equations were parabolas for question 1 above but for problem 4.3 the graphs were curves and they weren't like a parabola. 
 *  After the second difference found from a table you always find that a  quadratic
 * Square numbers: s=n^2
 * Rectangular numbers: r= n(n+1)
 * Area of a rectangle with a perimeter of 20: A=(10-L )L
 * Number of high fives: h= n/2(n-1)
 * A flea jump: H= -16t^2+8t
 * A. Make a table for each quadratic equation below. Use integer values of x from -5 to 5. Add columns to
 * 1. The patterns of differences for quadratic functions are not like the patterns of differences for the linear
 * b. For each table, look at the pattern of change in the y value as the x value increases by 1. How are the
 * c. How are the patterns of change in the tables reflected in the equations?**
 * 2. You have seen that a parabola is a symmetric shape with either a maximum point or a minimum point.