Concept explainers
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 y-value, so try Ymin = –130. Experiment with Ymax until your utility shows the parabola's major features.
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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