Polynomial Graphing Flashcard

Front

What is a cubic polynomial?

Back

A cubic polynomial is a polynomial of degree three, which can be expressed in the form k(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What is the end behavior of a polynomial?

Back

The end behavior of a polynomial describes how the values of the polynomial behave as x approaches positive or negative infinity.

Front

How do you identify the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

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.

Front

What does it mean for a polynomial to rise to positive infinity?

Back

It means that as x increases (approaches positive infinity), the value of the polynomial also increases without bound.

Front

What does it mean for a polynomial to decrease to negative infinity?

Back

It means that as x increases (approaches positive infinity), the value of the polynomial decreases without bound.

Front

What is the significance of the sign of the leading coefficient in determining end behavior?

Back

If the leading coefficient is positive, the polynomial will rise to positive infinity as x approaches positive infinity. If it is negative, the polynomial will fall to negative infinity.

Front

What is a quartic polynomial?

Back

A quartic polynomial is a polynomial of degree four, expressed in the form k(x) = ax^4 + bx^3 + cx^2 + dx + e, where a ≠ 0.

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree two, expressed in the form k(x) = ax^2 + bx + c, where a ≠ 0.

Front

What is a linear polynomial?

Back

A linear polynomial is a polynomial of degree one, expressed in the form k(x) = ax + b, where a ≠ 0.