Polynomial Graphs

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What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is: f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It determines the end behavior of the graph.

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What does the degree of a polynomial indicate?

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The degree of a polynomial is the highest power of the variable in the polynomial. It indicates the number of roots (zeros) the polynomial can have.

Front

How do you find the zeros of a polynomial function?

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To find the zeros of a polynomial function, set the function equal to zero and solve for the variable. The solutions are the x-values where the graph intersects the x-axis.

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What is the multiplicity of a zero?

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The multiplicity of a zero refers to the number of times a particular root appears in the polynomial. A zero with an even multiplicity will touch the x-axis, while a zero with an odd multiplicity will cross the x-axis.

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What is the difference between even and odd degree polynomials?

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Even degree polynomials have a symmetric graph about the y-axis, while odd degree polynomials have a graph that is symmetric about the origin.

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What is the end behavior of a polynomial function?

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The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity, determined by the leading coefficient and the degree.

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What is a trinomial?

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A trinomial is a polynomial with exactly three terms, which can be in the form of ax^2 + bx + c.

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What is a polynomial of degree 5?

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A polynomial of degree 5 is a polynomial where the highest exponent of the variable is 5, such as f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f.

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How do you identify a polynomial function from a graph?

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A polynomial function's graph is continuous and smooth, with no breaks, holes, or sharp corners.