6.5 Solving and Graphing Absolute Value Equations

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Solving and Graphing Absolute-Value Equations and Inequalities 2-8,9

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Presentation transcript:

6.5 Solving and Graphing Absolute Value Equations The equation |ax + b | = c where c ≥ 0 (positive) is equivalent to the statement: ax + b = c OR ax + b = -c Example: |3| = 3 and |-3| = 3 so, if |x| = 3 then x = 3 or -3

I. Solve Get absolute value by itself, make a disjunction, solve 1) |r-7| = 9 2) 2|x| + 4.1 = 18.9

I. Solve Continued 3) 4|m + 9| - 5 = 19 4) 2|p - 5| + 4 = 2

I. Solve Continued 5) 1/3 |2c - 5 | + 3 = 7

II. Absolute deviation: absolute deviation = |x - given value| 6) The absolute deviation of x from 7.6 is 5.2. What are the values of x that satisfy this requirement?

II. Absolute deviation Continued Five times the absolute deviation of 2x from -9 is 15. (Write and solve)

II. Absolute deviation Continued 8) A cheerleading squad is preparing a dance program for a competition. The program must last 4 minutes with an absolute deviation of 5 seconds. Write and solve an absolute value equation to find the least and greatest possible times (in seconds) that the program can last.

“Graphing Absolute Value Functions” 6.5 Extension Notes “Graphing Absolute Value Functions”

III. Graphing absolute value functions Set up a table and graph: 9) f(x) = |x| xx y -2 -1 1 2

III. Graphing absolute value functions Continued Set up a table and graph: 10) f(x) = |x| - 2 xx y -2 -1 1 2

III. Graphing absolute value functions Continued Set up a table and graph: 11) f(x) = 2|x| xx y -2 -1 1 2

III. Graphing absolute value functions Continued Set up a table and graph: 12) f(x) = -2|x| xx y -2 -1 1 2

III. Graphing absolute value functions Continued Set up a table and graph: 13) f(x) = |x - 2| Note: extra points needed xx y -2 -1 1 2

Graphing Summary f(x) = | x | (basic absolute function- V) f(x) = | x | + k (moves up or down) f(x) = | x - h| (moves left or right) f(x) = a| x | (open down if a is negative) (makes skinny or wide- think like slope)

Homework (20 problems) 6.5 Pages 393-395 # 4, 8, 10, 14, 16, 20, 22, 24, 28, 34, 38, 42, 44, 46, 48, 52 6.5 Extension Page 397 # 1-4 all (graph paper needed)