EXAMPLE 5 Standardized Test Practice How would the graph of the function y = x 2 + 6 be affected if the function were changed to y = x 2 + 2? A The graph.

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EXAMPLE 5 Standardized Test Practice How would the graph of the function y = x be affected if the function were changed to y = x 2 + 2? A The graph would shift 2 units up. B The graph would shift 4 units up. C The graph would shift 4 units down. D The graph would shift 4 units to the left.

EXAMPLE 5 Standardized Test Practice SOLUTION The vertex of the graph of y = x is 6 units above the origin, or (0, 6). The vertex of the graph of y = x is 2 units above the origin, or (0, 2). Moving the vertex from (0, 6) to (0, 2) translates the graph 4 units down. ANSWER The correct answer is C. A BC D

EXAMPLE 6 Use a graph SOLAR ENERGY A solar trough has a reflective parabolic surface that is used to collect solar energy. The sun’s rays are reflected from the surface toward a pipe that carries water. The heated water produces steam that is used to produce electricity. The graph of the function y = 0.09x 2 models the cross section of the reflective surface where x and y are measured in meters. Use the graph to find the domain and range of the function in this situation.

EXAMPLE 6 Use a graph SOLUTION STEP 1 Find the domain. In the graph, the reflective surface extends 5 meters on either side of the origin. So, the domain is  5 ≤ x ≤ 5. STEP 2 Find the range using the fact that the lowest point on the reflective surface is (0, 0) and the highest point, 5, occurs at each end. y = 0.09(5) 2 = 2.25 Substitute 5 for x. Then simplify. The range is 0 ≤ y ≤ 2.25.

GUIDED PRACTICE for Examples 5 and 6 Describe how the graph of the function y = x 2 +2 would be affected if the function were changed to y = x 2 – ANSWER The graph would be translated 4 units down. Domain: – 4 ≤ x ≤ 4, Range: 0 ≤y ≤1.44 ANSWER WHAT IF? In Example 6, suppose the reflective surface extends just 4 meters on either side of the origin. Find the domain and range of the function in this situation. 8.