Evaluate the expression for x = -6 1)|x|2) - | x – 3 | 3) | 1 – x | + 44) -3 | x + 4 | – Warm - up

2.5 Absolute Value Functions and Graphs CA State Standard Students solve equations and inequalities involving absolute value Objective – To be able to graph absolute value functions.

Graphing Absolute Value Functions The graph of y = a|mx-h| + k has the following characteristics. The graph has vertex (h/m,k) and is symmetric in the line x = h/m. The graph is V-shaped. It opens up if a > 0 and down if a < 0. The graph is wider if |a| 1. Vertex – The lowest or highest defined point on the graph. (If graph opens up the vertex is at the bottom, and vice versa).

Example 1 Graph y = - |x – 1| + 1 y = a|mx - h| + k What is the vertex? (h/m,k) = (1,1) Then plot another point on graph like x = 2 y = - |(2) – 1| + 1 y = 0 –5–4–3–2– –5 –4 –3 –2 – Use symmetry to plot a third point.

Example 2 Graph y = |x – 2| – 3 What is the vertex? (h,k) = (2,-3) Then plot another point on graph like x = 3 y = |(3) – 2| – 3 y = -2 –5–4–3–2– –5 –4 –3 –2 – Use symmetry to plot a third point.

Extra Example 2 Write an equation of the graph shown. What is the vertex? (h/m,k) = (0,2) Is our “a” value positive or negative? Why? Positive because it opens upward. y = ½|x| + 2 –5–4–3–2– –5 –4 –3 –2 – What do you notice about the slope? It is 1/2

Pg. 92 – 93 33, 35, 39, and 43

Due Thursday: Pg. 92 – 93 19, 22, 25, 29, 31, 40, 42 and 46