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Cubic Functions

Authored by Crystal Rivera

Mathematics

9th - 12th Grade

CCSS covered

Used 88+ times

Cubic Functions
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This quiz comprehensively covers cubic functions and polynomial analysis at the high school Algebra 2 level, specifically grades 9-12. Students work with multiple representations of cubic functions, including factored form, standard form, and graphical interpretations. The questions assess critical skills in finding roots and zeros of polynomials, identifying x-intercepts and y-intercepts, analyzing transformations of parent functions, and understanding domain and range properties. Students must demonstrate proficiency in working with factored forms like f(x) = (x+1)(x-4)(x+2), interpreting transformations such as reflections, translations, and compressions in expressions like y = -½(x + 4)³ - 1, and connecting algebraic representations to their graphical counterparts. The quiz also requires understanding of specialized vocabulary, including the relationship between roots, zeros, and x-intercepts, as well as concepts like points of inflection that are fundamental to cubic function behavior. Created by Crystal Rivera, a Mathematics teacher in US who teaches grade 9-12. This assessment serves as an excellent tool for formative evaluation, homework assignments, or review sessions when students are mastering polynomial functions and their properties. Teachers can use this quiz as a warm-up activity to gauge student readiness before introducing more complex polynomial topics, or as practice material to reinforce key concepts after initial instruction. The variety of question formats, from algebraic manipulation to graphical analysis, makes it particularly valuable for mixed-ability classrooms where students benefit from multiple approaches to the same mathematical concepts. The quiz aligns with Common Core standards A-APR.3 for identifying zeros of polynomials and using them to construct rough graphs, A-SSE.3 for analyzing function structure and transformations, and F-IF.7 for graphing polynomial functions and analyzing their key features, supporting comprehensive understanding of cubic functions within the broader algebra curriculum.

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25 questions

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1.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Media Image

What is the y-intercept of the following cubic function?

(1, 0)
(0, 2)
(-1, 0)
(2, 0)

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

2.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Determine the roots of the polynomial. 
f(x) = (x+1)(x-4)(x+2)

1, 4, 2
-1, -4, -2
1, -4, 2
-1, 4, -2

Tags

CCSS.HSF-IF.C.7C

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Describe the transformation of the graph  y = -(x - 4)3 + 5

Up 5 and Left 4 
Reflect x-axis, Left 4, Up 5
Reflect x-axis, Right 4, Up 5
Right 4 and up 5

Tags

CCSS.HSF.BF.B.3

4.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Describe the transformation of the graph  y = (x)3  + 6

Right 6
Left 6
Up 6
Down 6

Tags

CCSS.HSF.BF.B.3

5.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Describe the transformation of the graph  y = - ½(x + 4)3 - 1

Left 4 and Down 1
Reflected x-axis, Down 1, Left 4, Compression by a factor of 1/2
Reflected x-axis, Down 1, Left 4, Stretch by 1/2
Reflected x-axis, Up 1, Right 4, Compression by a factor of 1/2

Tags

CCSS.HSF.BF.B.3

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Determine the roots of the polynomial. 
f(x) = (x-2)(x+3)2

2, 3
2, -3
-2, 3
-2, 3, 3

Tags

CCSS.HSF-IF.C.7C

7.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Determine the roots of the polynomial. 
f(x) = -x(x+1)(x-3)

-1, 3
0, -1, 3
1, -3
0, -3, 1

Tags

CCSS.HSF-IF.C.7C

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