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messersmith_power_intermediate_algebra_1e_ch4_7_10

YOU TRY 1 Graph g(x) x2 1. Now let’s look at how we can shift the parabola f (x) x2 horizontally. EXAMPLE 2 Graph f (x) x2 and g(x) (x 3)2 on the same axes. Solution g(x) (x 3) left 3 f (x) x2 2 x left 3 y 7 3 Vertex Vertex 5 f(x) x2 x f(x) 0 0 1 1 2 4 1 1 2 4 g(x) (x 3)2 x g(x) 3 0 2 1 1 4 4 1 5 4 The functions f (x) and g(x) each have a domain of (q, q). Each has a range of 0, q). Notice that the y-values are the same in each table. The corresponding x-values in the table for g(x), however, are 3 less than the x-values in the fi rst table. The x-coordinates of the ordered pairs of g(x) are 3 less than the x-coordinates of the ordered pairs of f (x) when the ordered pairs of f and g have the same y-coordinates. This means that the graph of g is the same shape as the graph of f, but g is shifted left 3 units. Property Horizontal Shifts Given the graph of f (x), if g(x) f (x h), where h is a constant, then the graph of g(x) is the same shape as the graph of f (x) but g is shifted horizontally h units. We can think of Example 2 in terms of this horizontal shift. Since f (x) x2 and g(x) (x 3)2, h 3 in g(x) because we can think of g(x) as g(x) (x (3))2. The graph of g is the same shape as the graph of f but g is shifted 3 units horizontally or 3 units to the left. Note This vertical and horizontal shifting works for any function, not just quadratic functions. In your own words, describe how to shift a graph horizontally. YOU TRY 2 Graph g(x) (x 4)2. www.mhhe.com/messersmith SECTION 10.5 Quadratic Functions and Their Graphs 655


messersmith_power_intermediate_algebra_1e_ch4_7_10
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