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What is meant by the end behavior of a polynomial function?

Describe how to find a parabola's vertex if its equation is expressed in standard form. Give an example.

Explain how to use the Leading Coefficient Test to determine the end behavior of a polynomial function.

Why is a third-degree polynomial function with a negative leading coefficient not appropriate for modeling nonnegative real-world phenomena over a long period of time?

What is a rational inequality?

Explain the relationship between the multiplicity of a zero and whether or not the graph crosses or touches the \(x\) -axis and turns around at that zero.

a. Use a graphing utility to graph \(y=2 x^{2}-82 x+720\) 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 \(\mathrm{Xmin}=0\) and \(\mathrm{Xmax}=30 .\) The setting for \(y\) should include (and probably go below) the \(y\) -coordinate of the graph's minimum \(y\) -value, so try \(\mathrm{Ymin}=-130\) 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.

Explain the relationship between the degree of a polynomial function and the number of turning points on its graph.

Find the vertex for each parabola. Then determine a reasonable viewing rectangle on your graphing utility and use it to graph the quadratic function. $$y=5 x^{2}+40 x+600$$

Find the vertex for each parabola. Then determine a reasonable viewing rectangle on your graphing utility and use it to graph the quadratic function. $$y=0.01 x^{2}+0.6 x+100$$