Graphing Polynomials

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 2x^3 - 4x + 7 is a polynomial.

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How do you determine if a polynomial is odd or even?

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A polynomial is even if all its terms have even degrees and odd if all its terms have odd degrees. If it has both, it is neither.

Tags

CCSS.HSF.BF.B.3

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the expression. For example, in f(x) = 4x^5 - 3x^2 + 2, the degree is 5.

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What does the end behavior of a polynomial describe?

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The end behavior of a polynomial describes how the values of the polynomial behave as the input approaches positive or negative infinity.

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What is a y-intercept?

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The y-intercept of a polynomial is the point where the graph intersects the y-axis, found by evaluating the polynomial at x=0.

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What is a zero of a polynomial?

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A zero of a polynomial is a value of x that makes the polynomial equal to zero. For example, if f(x) = x^2 - 4, then x=2 and x=-2 are zeros.

Tags

CCSS.HSF-IF.C.7C

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What is multiplicity in relation to polynomial zeros?

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Multiplicity refers to the number of times a particular zero appears in a polynomial. For example, if (x - 3)^2 is a factor, then 3 is a zero with multiplicity 2.

Tags

CCSS.HSF-IF.C.7C

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How do you find the zeros of a polynomial?

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To find the zeros of a polynomial, set the polynomial equal to zero and solve for x. This can involve factoring, using the quadratic formula, or other methods.

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What is the significance of the leading coefficient in a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree. It affects the end behavior of the polynomial's graph.

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What is the relationship between the degree of a polynomial and the number of zeros?

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A polynomial of degree n can have up to n real zeros, counting multiplicities.