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77. a. Use a graphing utility to graph y = 2x2 – 82x + 720 in a standard viewing rectangle. What do you observe? b. Find the coordinates of the vertex for the given quadratic function. c. The answer to part (b) is (20.5, – 120.5). Because the leading coefficient, 2, of the given function is positive, the vertex is a minimum point on the graph. Use this fact to help find a viewing rectangle that will give a relatively complete picture of the parabola. With an axis of symmetry at x = 20.5, the setting for x should extend past this, so try Xmin = 0 and Xmax = 30. The setting for y should include (and probably go below) the y-coordinate of the graph's minimum point, so try Ymin = -130. Experiment with Ymax until your utility shows the parabola's major features. %3D %3D d. In general, explain how knowing the coordinates of a parabola's vertex can help determine a reasonable viewing rectangle on a graphing utility for obtaining a complete picture of the parabola.

77. a. Use a graphing utility to graph y = 2x2 – 82x + 720 in a standard viewing rectangle. What do you observe? b. Find the coordinates of the vertex for the given quadratic function. c. The answer to part (b) is (20.5, – 120.5). Because the leading coefficient, 2, of the given function is positive, the vertex is a minimum point on the graph. Use this fact to help find a viewing rectangle that will give a relatively complete picture of the parabola. With an axis of symmetry at x = 20.5, the setting for x should extend past this, so try Xmin = 0 and Xmax = 30. The setting for y should include (and probably go below) the y-coordinate of the graph's minimum point, so try Ymin = -130. Experiment with Ymax until your utility shows the parabola's major features. %3D %3D d. In general, explain how knowing the coordinates of a parabola's vertex can help determine a reasonable viewing rectangle on a graphing utility for obtaining a complete picture of the parabola.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.2: Transformations Of Quadratic Functions
Problem 42HP
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77. a. Use a graphing utility to graph y = 2x2 – 82x + 720 in a standard viewing rectangle. What do you observe? b. Find the coordinates of the vertex for the given quadratic function. c. The answer to part (b) is (20.5, – 120.5). Because the leading coefficient, 2, of the given function is positive, the vertex is a minimum point on the graph. Use this fact to help find a viewing rectangle that will give a relatively complete picture of the parabola. With an axis of symmetry at x = 20.5, the setting for x should extend past this, so try Xmin = 0 and Xmax = 30. The setting for y should include (and probably go below) the y-coordinate of the graph's minimum point, so try Ymin = -130. Experiment with Ymax until your utility shows the parabola's major features. %3D %3D d. In general, explain how knowing the coordinates of a parabola's vertex can help determine a reasonable viewing rectangle on a graphing utility for obtaining a complete picture of the parabola.
Transcribed Image Text:77. a. Use a graphing utility to graph y = 2x2 – 82x + 720 in a standard viewing rectangle. What do you observe? b. Find the coordinates of the vertex for the given quadratic function. c. The answer to part (b) is (20.5, – 120.5). Because the leading coefficient, 2, of the given function is positive, the vertex is a minimum point on the graph. Use this fact to help find a viewing rectangle that will give a relatively complete picture of the parabola. With an axis of symmetry at x = 20.5, the setting for x should extend past this, so try Xmin = 0 and Xmax = 30. The setting for y should include (and probably go below) the y-coordinate of the graph's minimum point, so try Ymin = -130. Experiment with Ymax until your utility shows the parabola's major features. %3D %3D d. In general, explain how knowing the coordinates of a parabola's vertex can help determine a reasonable viewing rectangle on a graphing utility for obtaining a complete picture of the parabola.
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