Graphing Polynomials in Factored Form

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What is the equation in factored form of a polynomial?

Back

An equation in factored form expresses a polynomial as a product of its factors, such as f(x) = (x - r1)(x - r2)...(x - rn), where r1, r2, ..., rn are the roots of the polynomial.

Front

What does the end-behavior of a polynomial function refer to?

Back

The end-behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity.

Front

How do you find the y-intercept of a polynomial function?

Back

To find the y-intercept of a polynomial function, evaluate the function at x = 0.

Front

What is the significance of the degree of a polynomial function?

Back

The degree of a polynomial function indicates the highest power of x in the polynomial, which affects the function's end-behavior and the number of real zeros.

Front

What does it mean for a polynomial function to have a positive leading coefficient?

Back

A polynomial function with a positive leading coefficient will rise to positive infinity as x approaches positive infinity.

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What is a real zero of a polynomial function?

Back

A real zero of a polynomial function is a value of x for which the function evaluates to zero, indicating an x-intercept on the graph.

Front

How can you determine the number of real zeros from the degree of a polynomial?

Back

The maximum number of real zeros of a polynomial function is equal to its degree.

Front

What is the relationship between the degree of a polynomial and its end-behavior?

Back

The end-behavior of a polynomial function is determined by its degree and the sign of its leading coefficient.

Front

What is the factored form of f(x) = x^2 - 5x + 6?

Back

f(x) = (x - 2)(x - 3) is the factored form of the polynomial.

Front

How do you identify the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial.