Polynomial Graphs

Front

What is a polynomial graph?

Back

A polynomial graph is the graphical representation of a polynomial function, which is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What does the degree of a polynomial indicate?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial. It determines the shape and number of turns in the graph.

Front

What is the difference between even and odd degree polynomials?

Back

Even degree polynomials have graphs that are symmetric about the y-axis, while odd degree polynomials have graphs that are symmetric about the origin.

Front

How can you determine if a polynomial has a maximum or minimum?

Back

You can determine if a polynomial has a maximum or minimum by analyzing its critical points, which are found by taking the derivative and setting it to zero.

Front

What is a real zero of a polynomial?

Back

A real zero of a polynomial is a value of x for which the polynomial evaluates to zero, indicating where the graph intersects the x-axis.

Front

How many turning points can a polynomial graph have?

Back

A polynomial graph can have at most n-1 turning points, where n is the degree of the polynomial.

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the graph behaves as x approaches positive or negative infinity, determined by the leading term.

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, which influences the graph's direction.

Front

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

Back

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

Front

What is the significance of the y-intercept in a polynomial graph?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the polynomial at x=0.