Polynomial Functions and Their Graphs: Algebra 2 Math Quiz – PDF Download
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.
🎯 Polynomial Functions and Their Graphs – Algebra 2 math quiz
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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 \(f(x)=-2x^{4}+x^{3}\)?
Arises on the left, rises on the right
Bfalls on the left, rises on the right
Crises on the left, falls on the right
Dfalls 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?
AIt touches the axis and turns around.
BIt crosses the axis like a straight line.
CIt flattens and crosses the x-axis.
DIt 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!
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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.
