HPC Unit 7 Polynomial & Rational Functions Review

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 polynomial function.

Front

What does a root with a multiplicity of 2 indicate about its graph?

Back

A root with a multiplicity of 2 indicates that the graph touches the x-axis at that root but does not cross it, creating a 'bounce' effect.

Front

What is the end behavior of a polynomial function as x approaches -∞ if the leading coefficient is negative and the degree is even?

Back

The end behavior will be f(x) → ∞ as x → -∞.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex of a quadratic function f(x) = ax^2 + bx + c can be found using the formula: Vertex = (-b/(2a), f(-b/(2a))).

Front

Back

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable and determines the number of roots and the end behavior of the polynomial function.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior is determined by the leading coefficient and the degree of the polynomial. If the degree is even, both ends will go in the same direction; if odd, they will go in opposite directions.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n, a_{n-1}, ..., a_0 are constants and n is a non-negative integer.

Front

What does it mean for a polynomial to be factored completely?

Back

A polynomial is factored completely when it is expressed as a product of its linear factors and irreducible polynomials, with no further factoring possible.

Front

What is the relationship between the roots and the factors of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and each root corresponds to a factor of the polynomial in the form (x - root).