Function Analysis

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.

Front

What does a positive leading coefficient indicate about the end behavior of a polynomial function?

Back

If a polynomial has a positive leading coefficient and an even degree, the ends of the graph will rise in both directions.

Front

What does a negative leading coefficient indicate about the end behavior of a polynomial function?

Back

If a polynomial has a negative leading coefficient and an even degree, the ends of the graph will fall in both directions.

Front

How do you find the roots of a quadratic function?

Back

To find the roots of a quadratic function ax^2 + bx + c = 0, use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

A polynomial function of degree n can have a maximum of n-1 turns.

Front

What is the end behavior of a polynomial function?

Back

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

Front

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

Back

The roots of a polynomial function are the x-values where the function equals zero, indicating where the graph intersects the x-axis.

Front

What is the difference between even and odd degree polynomials?

Back

Even degree polynomials have symmetrical end behavior, while odd degree polynomials have opposite end behavior.

Front

How can you determine the number of real roots a polynomial has?

Back

The number of real roots can be determined using the discriminant (b² - 4ac) for quadratics or by analyzing the function's graph.

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.