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In this lesson, we explore absolute value functions, focusing on graphing, identifying vertices, and using symmetry. We begin with the function y = |x + 4| - 8, identifying the vertex at (-4, -8) and plotting points, including (0, -4) and its symmetric counterpart (-8, -4). We also discuss the properties of the function y = -3|x - 1| + 2, noting its vertex at (1, 2), its downward opening, and a vertical stretch by a factor of 3. Learn to analyze and create equations for absolute value graphs through practical examples.
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2.7 Objective; _____To graph and write absolute value functions_
Check point; In the graph y=|x+4|-8, name the vertex. _____ (-4, -8)________ Plot another point on the graph. ___(0, -4)_ Use symmetry to find a third point _(-8, -4)_ and sketch the graph.
Check point; Tell what you know about the graph before plotting any points. y= -3|x-1| +2 Vertex; __(1,2)_ opens; _ down__ stretch or shrunk stretch by a factor of 3 point ___(0,-1)__ for all functions y= a∙f(x-h)+k stretch (if a>1) or shrink(if a<1) Vertex (h,k) also turn up (if a is positive) or down (if a is negative)
Write the equation of the shown graph. • 1. 2. • (1,4) • (1,2) (0,2) • (-1,0) • y = a |x – h| + k y = a |x – h| + k • y = a |x – 1| + 2 y = a |x – 0| + 2 • 0 = a |-1 – 1| + 2 4 = a |1 – 0| + 2 • 0 = a | – 2| + 2 4 = a |1 | + 2 • 0 = 2a + 2 4 = a + 2 • -2 = 2a 2 = a • -1 = a • y = -1 |x – 1| + 2 y = 2 |x | + 2
