2.2 Graphing Polynomials (PC1)

Front

What is the general form of a polynomial function?

Back

A polynomial function is expressed as f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0 and n is a non-negative integer.

Front

What does it mean for a polynomial to be in factored form?

Back

A polynomial is in factored form when it is expressed as a product of its linear factors, such as f(x) = (x - r1)(x - r2)...(x - rn), where r1, r2, ..., rn are the roots of the polynomial.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which f(x) = 0.

Front

How do you determine the multiplicity of a zero?

Back

The multiplicity of a zero is determined by the exponent of the corresponding factor in the polynomial's factored form.

Front

What is the effect of even multiplicity on the graph of a polynomial at a zero?

Back

If a zero has even multiplicity, the graph touches the x-axis at that zero but does not cross it.

Front

What is the effect of odd multiplicity on the graph of a polynomial at a zero?

Back

If a zero has odd multiplicity, the graph crosses the x-axis at that zero.

Front

What is the leading coefficient of a polynomial?

Back

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

Front

How does the leading coefficient affect the end behavior of a polynomial function?

Back

If the leading coefficient is positive, the graph rises to the right; if negative, it falls to the right.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

How can you find the x-intercepts of a polynomial function?

Back

To find the x-intercepts, set the polynomial equal to zero and solve for x.