Analyzing Graphs of Polynomial Functions

Algebra2: Section 6.8

With two other people:Each person pick a letter, f, g, or hEach person will graph their functionAfter graphing each function, discuss the following

questions with your partner:How many zeros does each graph have?How many turning points does each graph have?Is there a limit on the number of turning points a graph

will have?

The functions f(x) = 3 x⁵ - 2 x⁴ - 6 x³ + x² + 3 g(x) = 2 x⁵ - 3h(x) = x⁵ + x⁴ - 4 x³ - 3 x² + 5 x

Activity

The graph of every polynomial function of degree n has at most n – 1 turning points

If a polynomial function has n distinct real zeros, then its graph will have exactly n – 1 turning points

Turning Points of Polynomial Functions

Local MaximumHighest point on a curve

Local MinimumLowest point on a curve

EVERY turn or change of direction = local max/min

Is it possible for a point to be a zero and a local max/min?

HANDOUT

1. f(x) = 2 x⁴ - 5 x³ - 4 x² - 6

X-intercepts ≈ -1.16 and 3.21 Local min ≈ (2.31, -32.03) and (-0.43, -6.27) Local max ≈ (0, -6)

Examples: Graph Identify all x-intercepts and any local maximums or minimums.

P.377

# 29-34 allGRAPH & identify all x-intercepts and

any local maximums or minimums. (round to the nearest hundredth when

necessary)

Assignment