Zeros

Front

What is the end behavior of a polynomial function as x approaches infinity?

Back

As x approaches infinity, the end behavior of the graph can vary depending on the leading coefficient and degree of the polynomial. For even-degree polynomials with a positive leading coefficient, y approaches infinity. For odd-degree polynomials with a positive leading coefficient, y approaches infinity as x approaches infinity and y approaches negative infinity as x approaches negative infinity.

Front

What is the end behavior of a polynomial function as x approaches negative infinity?

Back

As x approaches negative infinity, the end behavior of the graph can vary depending on the leading coefficient and degree of the polynomial. For even-degree polynomials with a positive leading coefficient, y approaches infinity. For odd-degree polynomials with a positive leading coefficient, y approaches negative infinity as x approaches negative infinity.

Front

What is factored form of a polynomial?

Back

The factored form of a polynomial is an expression that represents the polynomial as a product of its linear factors. For example, f(x) = (x - r1)(x - r2)...(x - rn), where r1, r2, ..., rn are the roots or zeros of the polynomial.

Front

How do you find the zeros of a polynomial function?

Back

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

Tags

CCSS.HSF-IF.C.7C

Front

What does the multiplicity of a zero indicate?

Back

The multiplicity of a zero indicates how many times a particular zero appears as a root of the polynomial. A zero with an odd multiplicity will cross the x-axis, while a zero with an even multiplicity will touch the x-axis and turn around.

Front

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

Back

The leading coefficient determines the direction of the end behavior of the polynomial function. If the leading coefficient is positive, the graph will rise to the right; if it is negative, the graph will fall to the right.

Front

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

Back

The degree of a polynomial indicates the maximum number of zeros it can have. A polynomial of degree n can have up to n real zeros.

Front

How can you determine the number of turning points in a polynomial graph?

Back

The maximum number of turning points in a polynomial graph is one less than the degree of the polynomial. For example, a polynomial of degree 4 can have up to 3 turning points.

Front

What is the role of the x-intercepts in the graph of a polynomial function?

Back

The x-intercepts of a polynomial function are the points where the graph crosses or touches the x-axis. These points correspond to the zeros of the function.

Front

What is the difference between a zero and an x-intercept?

Back

A zero of a polynomial function is a value of x that makes the function equal to zero, while an x-intercept is the point on the graph where the function crosses the x-axis. They are often the same, but the term 'zero' refers to the value, while 'x-intercept' refers to the point.

Tags

CCSS.HSF-IF.C.7C