Polynomial Graphs Flashcard Part 1

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 is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial f(x) = 2x^4 + 3x^2 + 1, the degree is 4.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient is the coefficient of the term with the highest degree. It determines the end behavior of the polynomial graph. If it's positive, the graph rises to the right; if negative, it falls to the right.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable. The solutions are the x-values where the graph intersects the x-axis.

Front

What is the y-intercept of a polynomial function?

Back

The y-intercept of a polynomial function is the value of the function when x = 0. It can be found by evaluating f(0).

Front

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

Back

A polynomial graph can have a maximum of n-1 turns, where n is the degree of the polynomial.

Front

What is the significance of the zeros of a polynomial?

Back

The zeros of a polynomial are the x-values where the graph intersects the x-axis. They indicate the solutions to the equation f(x) = 0.

Front

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

Back

The end behavior of a polynomial function is determined by the leading term. If the leading coefficient is positive and the degree is even, both ends rise; if odd, one end rises and the other falls.

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 roots.

Front

What is the vertex of a quadratic polynomial?

Back

The vertex of a quadratic polynomial in the form f(x) = ax^2 + bx + c is the point (h, k) where h = -b/(2a) and k = f(h). It represents the maximum or minimum point of the graph.