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Polynomial Functions

Polynomial Functions. To the n th degree!. What are we trying to do?. Be able to look at any single-variable (only x, or only y, or only µ, or whatever) polynomial equation and be able to tell: The degree (should be review) The number of maxima or minima (Points of Inflection)

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Polynomial Functions

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  1. Polynomial Functions To the nth degree!

  2. What are we trying to do? • Be able to look at any single-variable (only x, or only y, or only µ, or whatever) polynomial equation and be able to tell: • The degree (should be review) • The number of maxima or minima (Points of Inflection) • The number of zeroes (real and imaginary roots)

  3. Constant Function • A variable equals a number • Forms a line perpendicular to the axis being used • No Points of Inflection – no curving • No Roots (never goes up or down to cross the axis) • x = 2 • y = -5

  4. Linear • f(x) = mx + b • A line passing through (0, b) with a slope of m • No points of inflection – no curving • 1 zero (root) – crosses the axis once • f(x) = 3x -2

  5. Quadratic • f(x) = ax2 + bx + c • What we were doing back in November • Parabolas • One Point of Inflection (PoI) • 2 real roots maximum • f(x) = 2x2 + 4x - 8

  6. Cubic • 3rd-order equations • Two PoIs • 3 real roots maximum • f(x) = 6x3 + 2x2 + 4x - 8

  7. Quartic • 4th-order equations • 3 P.o.I.s • 4 real roots maximum • f(x) = 9x4 + 6x3 + 2x2 + 4x - 8

  8. Quintic • 5th -order equations • 4 P.o.I.s • 5 real roots maximum • f(x) = 12x5 + 9x4 + 6x3 + 2x2 + 4x - 8

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