Polynomial Graphs - Characteristics

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What is a polynomial?

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

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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 polynomial. For example, in f(x) = 3x^2 + 4x - 5, the degree is 2.

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What is a relative minimum?

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A relative minimum is a point on the graph of a function where the function value is lower than the values of the function at nearby points. For example, in the graph of a polynomial, it is a local low point.

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What is the factored form of a polynomial?

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The factored form of a polynomial expresses it as a product of its factors. For example, f(x) = (x - 2)(x + 3) is a factored form of a polynomial.

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What does it mean for a polynomial to be quadratic?

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A polynomial is quadratic if its degree is 2. It can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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What is the range of a polynomial function?

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The range of a polynomial function is the set of all possible output values (y-values) that the function can produce. For example, the range of f(x) = x^2 is y ≥ 0.

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What is a root of a polynomial?

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A root of a polynomial is a value of x for which the polynomial equals zero. For example, if f(x) = x^2 - 4, the roots are x = 2 and x = -2.

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What is the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in f(x) = 5x^3 + 2x^2 - x + 7, the leading coefficient is 5.

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What is the end behavior of a polynomial?

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The end behavior of a polynomial describes how the values of the polynomial behave as x approaches positive or negative infinity. It is determined by the leading term.

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What is a turning point in a polynomial graph?

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A turning point is a point where the graph changes direction from increasing to decreasing or vice versa. It corresponds to local maxima and minima.