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

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

Assessment

Interactive Video

Mathematics

11th Grade - University

Hard

Created by

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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.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Coefficients

Y-intercepts

X-intercepts

Turning points

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Its magnitude

Its sign

Its multiplicity

Its degree

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the absolute maximum of a graph?

The highest x-value

The highest y-value

The lowest x-value

The lowest y-value

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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