Polynomial Graphs

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 2x^3 - 4x + 7 is a polynomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial f(x) = 3x^4 + 2x^2 - 5, the degree is 4.

Front

What are the zeroes of a polynomial?

Back

The zeroes of a polynomial are the values of x for which the polynomial equals zero. They are also known as the roots of the polynomial.

Front

How does the leading coefficient affect the graph of a polynomial?

Back

The leading coefficient determines the direction of the graph as x approaches positive or negative infinity. A positive leading coefficient means the graph rises to the right, while a negative leading coefficient means it falls to the right.

Front

What is end behavior in polynomial functions?

Back

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

Front

What is the significance of even and odd degrees in polynomials?

Back

Even degree polynomials have the same end behavior on both sides (both up or both down), while odd degree polynomials have opposite end behavior (one side up and the other down).

Front

How can you determine the number of zeroes from a polynomial graph?

Back

The number of zeroes can be determined by counting the x-intercepts of the graph. Each x-intercept corresponds to a zero of the polynomial.

Front

What does it mean if a polynomial has a double root?

Back

A double root means that the polynomial touches the x-axis at that point but does not cross it. This occurs when the factor corresponding to that root is squared.

Front

What is the relationship between the degree of a polynomial and the number of turning points?

Back

A polynomial of degree n can have at most n-1 turning points.

Front

What is a turning point in a polynomial graph?

Back

A turning point is a point on the graph where the function changes direction from increasing to decreasing or vice versa.