Determine whether the statement is sometimes, always, or never true Determine whether the statement is sometimes, always, or never true. The graph of a polynomial of degree three will intersect the x-axis three times. Draw a picture to illustrate the choice you made.

5-4 Analyzing Graphs of Polynomials Graph polynomial functions and locate their zeros Find relative maxima or minima of polynomial functions

Relative maxima: A point that is the highest point in its immediate vicinity. (Highest y-value) Top of the mountain Relative minima: A point that is the lowest point in its immediate vicinity. (Lowest y-value) Bottom of the valley Extrema: maximum and minimum values of a function (highs and lows) Turning points: another name for relative extrema – The graph of a polynomial function of degree n has AT MOST (n – 1) turning points.

To graph, make a table of values to find several points and then connect them to make a smooth, continuous curve. If you know end behaviors, you know when to shoot for infinity. A change of signs in the value of f(x) from one value of x to the next indicates that the graph of the function crosses the x-axis between the two x-values. A change between increasing values and decreasing values indicates that the graph is turning for that interval. A turning point on a graph is a relative maximum or minimum.

17. a) Graph by making a table of values (write down enough points to show where x-intercepts lie and where extrema (turning points) lie. b) Determine the consecutive integer values of x between which each real zero is located. c) Estimate the x-coordinates at which the relative maxima and minima occur. 𝑓 𝑥 = 𝑥 3 −5 𝑥 2 +3𝑥+1

Use a graphing calculator to estimate the x-values at which the maxima and minima of the function occur. Round to the nearest hundredth. 25. 𝑓 𝑥 = −2𝑥 4 +5 𝑥 3 −4 𝑥 2 +3𝑥 −7 (CALC, max or min, move to left, then right, enter, enter)