Algebra 2 Polynomial Functions Quiz – Free PDF

Contents

This algebra 2 polynomial functions quiz asks 10 multiple-choice questions on polynomial functions and their graphs, and each answer comes with a short explanation.

Try these ten multiple-choice questions on degree, end behavior, zeros, multiplicity, turning points and graphs of polynomial functions. Each question has exactly one correct answer, and the explanation points out the mistake that the wrong choices come from.

Algebra 2Common Core: F-IF.C.7c · A-APR.B.3 · F-IF.B.4

🎯 Polynomial Functions and Their Graphs – Algebra 2 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

What is the degree of \(f(x)=(x-1)(x+2)(3x+1)\)?

A \(1\)

B \(5\)

C \(3\)

D \(6\)

Question 2

What is the end behavior of \(f(x)=-2x^{4}+x^{3}\)?

A rises on the left, rises on the right

B falls on the left, rises on the right

C rises on the left, falls on the right

D falls on the left, falls on the right

Question 3

The function \(f(x)=(x-4)^{3}(x+1)^{2}\) has a zero at \(x=4\). How does the graph behave there?

A It touches the axis and turns around.

B It crosses the axis like a straight line.

C It flattens and crosses the x-axis.

D It never reaches the x-axis.

Question 4

What are the zeros of \(f(x)=x^{3}-x^{2}-6x\)?

A \(0,\ -3,\ 2\)

B \(3,\ -2\)

C \(0,\ 6,\ -1\)

D \(0,\ 3,\ -2\)

Question 5

What is the greatest number of turning points a polynomial of degree \(7\) can have?

A \(7\)

B \(6\)

C \(8\)

D \(5\)

Question 6

Which function could have the graph shown?

A cubic with three zeros.

A \(f(x)=(x-2)(x+1)(x+3)\)

B \(f(x)=(x+2)(x-1)(x-3)\)

C \(f(x)=-(x+2)(x-1)(x-3)\)

D \(f(x)=(x+2)(x-1)^{2}(x-3)\)

Question 7

At which zero does the graph touch the x-axis without crossing?

A cubic with a double zero.

A \(x=-1\)

B \(x=2\)

C \(x=0\)

D \(x=1\)

Question 8

A square of side x is cut from each corner of the 8-inch by 12-inch sheet to make an open box. Which domain makes sense for the volume function?

Not drawn to scale.

A \(0 < x < 4\)

B \(0 < x < 6\)

C \(0 < x < 8\)

D \(x>0\)

Question 9

Which function has zeros \(2\) and \(-3\), and a zero at \(-1\) with multiplicity \(2\), with least degree?

A \(f(x)=(x+2)(x-3)(x-1)^{2}\)

B \(f(x)=(x-2)(x+3)(x+1)^{2}\)

C \(f(x)=(x-2)(x+3)(x+1)\)

D \(f(x)=(x-2)(x+3)(x-1)^{2}\)

Question 10

For \(f(x)=x^{3}-3x+5\), what is \(f(-2)\)?

A \(-9\)

B \(7\)

C \(3\)

D \(19\)

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards F-IF.C.7c, A-APR.B.3 and F-IF.B.4: graph polynomials using zeros and end behavior, and interpret key features.
Even degree: both ends point the same way. Odd degree: the ends point opposite ways. The sign of \(a_{n}\) picks up or down.
A zero of odd multiplicity is a crossing; a zero of even multiplicity is a touch point.
A polynomial of degree \(n\) has at most \(n\) real zeros and at most \(n-1\) turning points.
The y-intercept of \(f\) is \(f(0)\); in factored form, multiply the constant parts.