Graphing Polynomials

Front

What determines the end behavior of a polynomial?

Back

The degree and the leading coefficient of the polynomial.

Front

What is the degree of a polynomial with a leading coefficient that is positive and even?

Back

The degree is even and the leading coefficient is positive.

Front

What are the zeros (x-intercepts) of the polynomial f(x) = x^3 - 6x^2 + 9x?

Back

The zeros are x = 2, -2, 0.

Front

Which polynomial could represent a graph with a positive leading coefficient and an odd degree?

Back

f(x) = x^3 + 6x^2 + 9x.

Front

What is the complete list of possible Rational Zeros for f(x) = 3x^3 + 2x^2 - 6x + 7?

Back

±1, ±7, ±1/3, ±7/3.

Front

Define a polynomial function.

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What is the leading coefficient of the polynomial f(x) = 4x^5 - 3x^3 + 2?

Back

The leading coefficient is 4.

Front

How do you find the x-intercepts of a polynomial?

Back

Set the polynomial equal to zero and solve for x.

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 affects the shape and end behavior of the graph.

Front

What does it mean if a polynomial has an even degree?

Back

If a polynomial has an even degree, its ends will rise or fall in the same direction as x approaches positive or negative infinity.