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Completing the Square (A) WORKSHEET
Suitable for Grades: Algebra II, IM 2
CCSS: HSA.REI.B.4.B, HSA.SSE.B.3.B
CCSS Description: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Completing the Square (A) WORKSHEET DESCRIPTION
This worksheet is designed to develop students' understanding of quadratic expressions and how they can be manipulated in different ways.
In Section A, students are introduced to perfect squares by expanding expressions such as (𝑥 + a)^2, where a is an integer, and matching equivalent expressions. This section builds their foundational knowledge and recognition of perfect squares.
Section B progresses the learning by providing students with an opportunity to expand and simplify expressions in the form (𝑥 + a)^2 + b, where a and b are integers, match up equivalent expressions, and then to write quadratic expressions in this form.
Section C extends this by introducing factorised expressions where a and b are fractions.
The worksheet culminates with an extension task that requires students to express a quadratic in the form a(𝑥 + b)^2 + c, applying their understanding to a new level of difficulty.
In Section A, students are introduced to perfect squares by expanding expressions such as (𝑥 + a)^2, where a is an integer, and matching equivalent expressions. This section builds their foundational knowledge and recognition of perfect squares.
Section B progresses the learning by providing students with an opportunity to expand and simplify expressions in the form (𝑥 + a)^2 + b, where a and b are integers, match up equivalent expressions, and then to write quadratic expressions in this form.
Section C extends this by introducing factorised expressions where a and b are fractions.
The worksheet culminates with an extension task that requires students to express a quadratic in the form a(𝑥 + b)^2 + c, applying their understanding to a new level of difficulty.
All worksheets are created by the team of experienced teachers at Cazoom Math.
Frequently Asked Questions
This completing the square (a) worksheet is designed for students in Algebra II and IM 2 and aligns with Common Core State Standards.