Complete the Square
Authored by Erin Muse _ Staff - SalemMS
Mathematics
9th - 12th Grade
CCSS covered
Used 815+ times
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About
This quiz focuses on the algebraic technique of completing the square for solving quadratic equations, targeted at the high school Algebra II level, typically grades 9-12. Students need a solid understanding of quadratic expressions, factoring perfect square trinomials, and manipulating algebraic equations to master this content. The questions systematically build from the foundational mechanics of completing the square—such as transforming the linear coefficient and isolating variable terms—to applying the complete process for solving various forms of quadratic equations. Students must demonstrate proficiency with radical simplification, understanding when to apply the plus-or-minus symbol, and working with equations that have both rational and irrational solutions. The complexity progresses from basic procedural steps to multi-step problem solving that requires students to combine completing the square with other algebraic skills. Created by Erin Muse, a Mathematics teacher in the US who teaches grades 9-12. This quiz serves as an excellent formative assessment tool to gauge student understanding of completing the square before moving to more advanced quadratic applications. Teachers can use this as a warm-up activity to review the method, as guided practice during instruction, or as homework to reinforce the step-by-step process students learned in class. The variety of question types—from conceptual understanding to procedural application—makes it valuable for identifying specific areas where students need additional support. This assessment aligns with standards A-REI.B.4, which requires students to solve quadratic equations by completing the square, and A-APR.B.3, which involves understanding the relationship between zeros and factors of polynomials.
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Student View
13 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What do you do to the b value to correctly complete the square?
Tags
CCSS.HSA-REI.B.4B
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
To solve by completing the square, what needs to be moved in this equation?
x2 = 9 - 4x
Tags
CCSS.HSA-REI.B.4B
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What is the first step to solving THIS equation by completing the square?
a2 + 10a + 21 = 0
Tags
CCSS.HSA-REI.B.4B
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
Tags
CCSS.HSA-REI.B.4B
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
When do you use the plus or minus symbol?
±
Tags
CCSS.HSA-REI.B.4B
6.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
What is one of the solutions to this equation?
(2x - 1)2 = 49
Tags
CCSS.HSA-REI.B.4B
7.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Solve the following equation by completing the square:
n2 - 2n - 3 = 0
Tags
CCSS.HSA-REI.B.4B
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