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.