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Algebra 2 2.6A Absolute Value Functions Obj: able to find the vertices of absolute value functions and graph them using a calculator. Recall the definition of absolute value from Chapter 1: The absolute value of a number is ___________________________________________. absolute value function – the function f(x) = | x |, or in linear equation format, y = | x |. This is a ‘V’ shaped graph where the point of the ‘V’ is called the vertex. finding the vertex of an absolute value function – let the expression inside the absolute value bars equal zero and solve for x. This x value is then the x-coordinate of the vertex. Once you know the value for x, use it in the linear equation format to find the value for y, which will be the y-coordinate of the vertex. 1. Find the vertex of the function y = | x | . Then complete the table and graph the function. Let x = 0, then | x |=0, and y= | 0 |, putting the vertex at (0, 0). vertex 2. x -2 -1 0 1 2 y 0 Find the vertex of the function y = | x | + 1. Then complete the table and graph the function. Let x = 0, then | x |=0, and y= | 0 | + 1, putting the vertex at (0, 1). vertex 3. x -2 -1 0 1 2 y 1 Find the vertex of the function y = | x + 1 | . Then complete the table and graph the function. Let x + 1= 0, then x = -1 makes | x + 1 |=0, and y= | 0 | , putting the vertex at (-1, 0). vertex x -2 -1 0 1 2 y 0 2.6A Cooperative Learning DIRECTIONS: With your partner, work out the following problems. You both need to record answers on your own page as you work together. Graphing Absolute Value Functions on the TI-83+ In the Y= screen, type in the equation y1 = | x | . To make the absolute value bar, press MATH, ► (NUM menu) and then 1: abs( . This takes you back to the Y= screen, so press X,T,Θ,n to enter the x variable, and then make sure to close off the absolute value by adding in the close parentheses ). Press ZOOM , 6: ZStandard to set the window at the standard 10 units nd in each direction from the origin and to see the graph. Press 2 , GRAPH to see a table of ordered pairs (x, y1) and (x, y2) for each of the functions Graph each pair of equations on a graphing calculator. Then sketch the pair on the same graph and label by problem #. 1. y1 = | x | 2. y2 = 2| x | 7. y1 = 3| x | 8. y2 = -3| x | 3. y1 = | x | + 2 4. y2 = | x | – 3 5. y1 = | x + 2 | 6. y2 = | x – 4 | The parent graph for absolute value functions is y = | x | with a vertex at (0, 0) A vertical translation occurs when y = | x | ± k, where k is a positive number. y = | x | + k translates the graph of the parent function _________ k units. y = | x | – k translates the graph of the parent function _________ k units. A horizontal translation occurs when y = | x ± h |, where h is a positive number. y = | x + h | translates the graph of the parent function _________ h units. y = | x – h | translates the graph of the parent function _________ h units. A combined translation occurs when y = | x ± h | ± k, where h and k are positive A stretch occurs when y = a| x ± h | ± k and a > 1 A reflection about the x-axis occurs when y = a| x ± h | ± k and a < 0 I don’t get it at all 1 What do you still need to work on? Rate yourself on how well you understood this lesson. I understand I sort of I understand most of it but I get it it pretty well need more practice 2 3 4 I got it! 5