CHAPTER TWO: LINEAR EQUATIONS AND FUNCTIONS ALGEBRA TWO CHAPTER TWO: LINEAR EQUATIONS AND FUNCTIONS Section 2.8 - Absolute Value Functions

LEARNING GOALS Goal One - Represent absolute value functions. Goal Two - Use absolute value functions to model real-life quantities.

VOCABULARY The absolute value function has the standard form of y = a|x - h| + k, and its graph has the following characteristics: The vertex occurs at the point (h, k), and the graph is symmetric in the line x = h. The graph is V-shaped and opens up if a > 0 and down if a < 0. The graph is wider than the graph of y = |x| if |a| < 1 and narrower if |a| > 1. 1

Graphing an Absolute Value Function Form: y = a|x - h| + k Step 1: plot the vertex (h, k) Step 2: Plot a second point: choose a value for x, and solve for y. This will give you your second point (x,y) Step 3: Use symmetry to plot a third point on the opposite side of the symmetry line x = h. Step 4: Connect these three points with a V-shaped graph

Graphing an Absolute Value Function PROBLEM: Graph y = 3|x - 2| - 4 First plot the vertex at (2, -4) Then plot another point, such as (1, -1). Use symmetry to plot a third point, (3, -1). Connect these three points with a V-shaped graph. Notice that a = 3 > 0 and |a| > 1, so the graph opens up and is narrower than y = |x|.

Graphing an Absolute Value Function PROBLEM: Graph y = 3|x - 2| - 4

Graphing an Absolute Value Function PROBLEM: Graph y = -2|x + 1| + 3 First plot the vertex at (-1, 3) Then plot another point, such as (0, 1). Use symmetry to plot a third point, (-2, 1). Connect these three points with a V-shaped graph. Notice that a = -2 < 0 and |a| > 1, so the graph opens down and is narrower than y = |x|.

Graphing an Absolute Value Function PROBLEM: Graph y = -2|x + 1| + 3

ASSIGNMENT READ & STUDY: pg. 122-124. WRITE: pg. 125-128. #19, #21, #23, #25, #35, #57, #59, #61, #63, & #65.