How to determine the extrema and zeros from the graph of a polynomial

The video tutorial covers polynomial concepts, focusing on zeros, multiplicity, degree, and leading coefficients. It explains how to write polynomials in factored form and identify absolute and relative extrema on graphs. The teacher emphasizes understanding these concepts through graphical representation and provides methods to determine polynomial characteristics.

What are the real zeros of a polynomial also known as?

• Coefficients

• Y-intercepts

• X-intercepts

• Turning points

What happens to the graph of a polynomial at a zero with an even multiplicity?

• It crosses the x-axis

• It remains constant

• It shifts vertically

• It bounces off the x-axis

How can you determine the degree of a polynomial by counting?

• The number of coefficients

• The number of x-intercepts

• The number of turning points plus one

• The number of terms

What does the end behavior of a graph indicate about the leading coefficient?

• Its magnitude

• Its sign

• Its multiplicity

• Its degree

How do you write a polynomial in factored form if you know its zeros?

• By using the same signs of the zeros

• By using the degree of the polynomial

• By using the leading coefficient

• By using the opposite signs of the zeros

What is the absolute maximum of a graph?

• The highest x-value

• The highest y-value

• The lowest x-value

• The lowest y-value

Why might a graph not have an absolute minimum?

• Because it extends infinitely downward

• Because it is a constant function

• Because it has no turning points

• Because it has no x-intercepts

What is a relative maximum?

• A low point at a turning point

• The lowest point on the entire graph

• A high point at a turning point

• The highest point on the entire graph

How is a relative minimum different from an absolute minimum?

• It is the lowest point in a local area

• It is the lowest point on the entire graph

• It is the highest point in a local area

• It is the highest point on the entire graph

What is the significance of a turning point in determining relative extrema?

• It shows the end behavior

• It marks a local high or low point

• It determines the leading coefficient

• It indicates a change in the degree