The changes in sign indicate that are zeros between = x –2 x f(x) and = and between = 1 and = 2. x x x –1 35 –2 –1 –2 0 –5 1 –4 2 19 Exercises Graph each function by making a table of values. Determine the values of between which each real zero is x located. 1. = 2 + 1 2. = + 2 5 3. = + 2 1 f(x) f(x) f(x) – – – – 4. = 3 + 4 5. = 3 + 2x 1 6. = 3 + 1 f(x) – f(x) – f(x) – 5-4 Study Guide and Intervention (continued) Analyzing Graphs of Polynomial Functions Maximum and Minimum Points A quadratic function has either a maximum or a minimum on its graph. For higher degree polynomial functions, you can find which represent relative maximum or relative turning points, minimum points. Example: Graph = + 6 3. Estimate the at which the relative maxima and minima occur. f(x) x-coordinates – Make a of values and graph the function. x f(x) 2 29 22 –5 A relative maximum occurs at 29 indicates a relative maximum –4 ← = and a relative minimum occurs at = 0. x –4 x 24 –3 13 –2 2 zero between x = x = 0 –1 ← –1, 0 a relative minimum ←indicates –3 1 4
x f(x) –2 35 –1 –2 0 –5 1 –4 2 19 The changes in sign indicate that are zeros between x = –2 and x = –1 and between x = 1 and x = 2. Exercises Graph each function by making a table of values. Determine the values of x between which each real zero is located. 1. f(x) = – 2 + 1 2. f(x) = + 2 – 5 3. f(x) = – + 2 – 1 4. f(x) = – 3 + 4 5. f(x) = 3 + 2x – 1 6. f(x) = – 3 + 1 5-4 Study Guide and Intervention (continued) Analyzing Graphs of Polynomial Functions Maximum and Minimum Points A quadratic function has either a maximum or a minimum on its graph. For higher degree polynomial functions, you can find turning points, which represent relative maximum or relative minimum points. Example: Graph f(x) = + 6 – 3. Estimate the x-coordinates at which the relative maxima and minima occur. Make a of values and graph the function. x f(x) –5 22 –4 29 ← indicates a relative maximum –3 24 –2 13 –1 2 ← zero between x = –1, x = 0 0 –3 ←indicates a relative minimum 1 4 2 29 A relative maximum occurs at x = –4 and a relative minimum occurs at x = 0.
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