Algebra 2 Polynomial Functions 3.1, 3.5

Front

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 a_n ≠ 0.

Front

What are the zeros of a polynomial function?

Back

The zeros of a polynomial function are the values of x for which the function f(x) = 0. They represent the x-intercepts of the graph of the function.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for x using factoring, the quadratic formula, or numerical methods.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression. It determines the polynomial's behavior and the maximum number of zeros.

Front

What is a leading coefficient?

Back

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

Front

What is the relationship between the degree of a polynomial and the number of possible zeros?

Back

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

Front

What is a relative minimum?

Back

A relative minimum is a point on the graph of a function where the function value is lower than the values of the function at nearby points.

Front

What is the maximum number of turns a polynomial graph can have?

Back

The maximum number of turns a polynomial graph can have is one less than its degree.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its linear factors. For example, f(x) = (x - r1)(x - r2)...(x - rn) where r1, r2, ..., rn are the zeros.

Front

How do you determine the number of real solutions of a quadratic equation?

Back

The number of real solutions can be determined using the discriminant (b^2 - 4ac). If the discriminant is positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.