Polynomial Graphs

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to whole number powers and coefficients, combined using addition, subtraction, and multiplication.

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 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 the factored form of a polynomial represent?

Back

The factored form of a polynomial expresses it as a product of its linear factors, which can help identify the roots or x-intercepts of the graph.

Front

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

Back

To find the x-intercepts, set the polynomial equal to zero and solve for x.

Front

What is the significance of the minimum value of a polynomial graph?

Back

The minimum value of a polynomial graph represents the lowest point on the graph, indicating the smallest output value of the function.

Front

What is end behavior in polynomial graphs?

Back

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

Front

How does the leading coefficient affect the end behavior of a polynomial?

Back

If the leading coefficient is positive, the graph rises to the right; if negative, it falls to the right.

Front

What is a root of a polynomial?

Back

A root of a polynomial is a value of x that makes the polynomial equal to zero.

Front

What is the difference between a linear factor and a quadratic factor?

Back

A linear factor is of the form (x - r), while a quadratic factor is of the form (ax^2 + bx + c) where a ≠ 0.