This algebra 2 polynomial test answer key gives the full solution and the scoring guide for each of the 8 test questions on polynomial functions and their graphs.
This key gives a complete solution and a scoring guide for every question. Award partial credit as described, and give full credit for any valid method that reaches a correct result, including equivalent forms of an equation.
Algebra 2 Polynomial Test Answer Key: questions 1–5
Question 1: Degree and end behavior (2 points)
- Degree \(5\), leading coefficient \(-3\).
- Odd degree, negative leading coefficient: rises on the left and falls on the right.
Scoring: 1 point for each part. Part a needs both values.
Question 2: Zeros and multiplicity (2 points)
- \(x=0\) (multiplicity \(1\)), \(x=2\) (multiplicity \(2\)), \(x=-5\) (multiplicity \(3\)).
- Degree \(1+2+3=\) \(6\). It crosses at \(0\), touches and turns at \(2\), and flattens and crosses at \(-5\).
Scoring: 1 point for each part. In part b, the degree and at least two correct behaviors are needed.
Question 3: Factor by grouping (2 points)
- \(x^{2}(x-4)-9(x-4)=(x-4)(x^{2}-9)=\) \((x-4)(x-3)(x+3)\).
- \(x=4,\ 3,\ -3\). Check: \(g(3)=27-36-27+36=0\).
Scoring: 1 point for each part.
Question 4: Equation from a graph (3 points)
- \(x=-1\) (multiplicity \(1\), crosses) and \(x=2\) (multiplicity \(2\), touches).
- \(f(x)=a(x+1)(x-2)^{2}\) and \(f(0)=a(1)(4)=-8\), so \(a=-2\).
- \(f(x)=-2(x+1)(x-2)^{2}\). Check: \(f(1)=-2(2)(1)=-4\).
Scoring: 1 point for each part. Allow follow-through from part a when computing the leading coefficient.
Question 5: Sketch a graph (3 points)
Zeros: \(-2\), \(0\) and \(3\), each crossing. Degree \(3\) with positive leading coefficient: falls on the left, rises on the right. Test values: \(f(-1)=4\), \(f(1)=-6\), \(f(2)=-8\).
Scoring: 1 point for the three zeros labeled; 1 point for correct end behavior; 1 point for a smooth curve with the right signs between the zeros.
Algebra 2 Polynomial Test Answer Key: questions 6–8
Question 6: Turning points (2 points)
- \(6-1=\) \(5\).
- The graph has \(3\) turning points, so the degree is at least \(4\). Both ends rise, so the degree is even and the leading coefficient is positive. Least degree \(4\).
Scoring: 1 point for each part. Part b needs both the degree and the sign.
Question 7: Trail elevation (3 points)
- \(e(x)=0\) at \(0,\ 2\) and \(6\) miles.
- The table values are negative from \(x=3\) to \(x=5\), and \(e\) is zero at \(2\) and \(6\): between \(2\) and \(6\) miles.
- \(-16\) feet at mile \(4\).
Scoring: 1 point for each part.
Question 8: Open box (3 points)
- Length \(15-2x\), width \(9-2x\), height \(x\): \(V(x)=x(9-2x)(15-2x)\).
- The width \(9-2x\) must be positive: \(0 < x < 4.5\).
- \(V(2)=2(5)(11)=110\) and \(V(3)=3(3)(9)=81\). \(x=2\) gives the greater volume.
Scoring: 1 point for each part.
Scoring summary
20 points: add the points of every question of this algebra 2 polynomial test answer key.
How to use this algebra 2 polynomial test answer key
Use this algebra 2 polynomial test answer key to score the test fairly and to see which skills need more practice.
Printable PDF · Test Answer Key
Algebra 2 Polynomial Functions and Their Graphs test answer key
Download the PDF
See every chapter on the Algebra 2 math page.
