Polynomials

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by SammyD9
Last updated 5 years ago

Discipline:
Math
Subject:
Pre-Calculus
Grade:
9

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Polynomials

End Behavior: f(x) -> ∞ as x -> -∞ f(x) -> -∞ as x -> ∞

-Relative Maximum: The relative maximum on a polynomial graph is the point(s) that have maximum y values relative to the points around them. -Relative Minimum: The relative minimum on a polynomial graph is the point(s) that have minimum y values relative to the points around them.

Polynomials

End Behavior: f(x) -> -∞ as x -> -∞f(x) -> ∞ as x -> ∞

Leading Coefficient and Degree: In a polynomial function, the coefficient with the highest degree is the leading coefficient. The leading degree is the highest exponent.

End Behavior: The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches negative infinity or positive infinity.

Negative Polynomial Functions

-Leading Coefficient = -7-Leading Degree = 2

Zeroes: In graphing polynomial functions, the zeroes (or roots) are the places at which the line crosses the x-axis.

Zeroes: between -1 and 0 (-0.84), between 1 and 2 (1.55)

-Absolute Maximum = 9-Absolute Minimum = -∞

-7x^2+5x+9

-x^3+3x^2-3

-Relative Maximum = 1-Relative Minimum = -3

Zeroes: between -1 and 0 (-0.87), between 1 and 2 (1.4), and between 2 and 3 (2.55)

-Leading Coefficient = -1-Leading Degree = 3

Positive Polynomial Functions

-Absolute Maximum = ∞ -Absolute Minimum = -1

-Leading Coefficient = 1-Leading Degree = 3

Zeroes: between 0 and 1 (0.3), between 1 and 2 (1.7)

Odd-degree function

-Leading Coefficient: 2-Leading Degree: 2

2x^2-4x+1

x^3-1.5x^2-6x+1

End Behavior: f(x) -> -∞ as x -> -∞f(x) -> ∞ as x -> ∞

End Behavior: f(x) -> ∞ as x -> -∞ f(x) -> ∞ as x -> ∞

Odd-degree function

Even-degree function

Even-degree function

-Relative Maximum = 5.5-Relative Minimum = -9

Zeroes: between -2 and -1 (-1.9), between 0 and 1 (0.17), and between 3 and 4 (3.24)

-Absolute Maximum: The absolute maximum of a polynomial graph is the point on the graph that has the highest value of y. -Absolute Minimum: The absolute minimum of a polynomial graph is the point on the graph that has the smallest value of y.


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