Graphs of Polynomial

Front

What is the end behavior of the polynomial function y = -x^3 + 6x^2 + 7x?

Back

As x -> -∞, f(x) -> ∞; as x -> ∞, f(x) -> -∞.

Front

What characterizes the graph of an even function with a positive leading coefficient?

Back

The graph is symmetric about the y-axis and opens upwards.

Front

What is the maximum number of solutions for the polynomial f(x) = 5x^4 + 2x^3 + 2x - 7?

Back

4 solutions.

Front

What is the factored form of the polynomial that corresponds to the graph shown?

Back

(x-5)^2(x-2)(x+3)

Front

List the zeros of the function f(x) = (x+4)(x-3)(x-2).

Back

x = -4, x = 3, x = 2.

Front

What is the degree of the polynomial function f(x) = 5x^4 + 2x^3 + 2x - 7?

Back

The degree is 4.

Front

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

Back

Look at the leading term's degree and coefficient.

Front

What does it mean for a polynomial to have a positive leading coefficient?

Back

The graph will rise to the right as x approaches infinity.

Front

What is the significance of the zeros of a polynomial function?

Back

Zeros are the x-values where the function intersects the x-axis.

Front

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

Back

A polynomial of degree n can have at most n real roots.