Completing the Square Color by Numbers Worksheet

Product description

From the author

Practice solving quadratic equations by completing the square with twelve problems and a color-coded answer bank. Students solve each equation, match the solution pair and color the corresponding picture regions.

The three-page PDF contains the problem sheet, numbered coloring picture and a completed colored picture that serves as the key. Ask students to retain their algebraic working for review.

In the classroom

Teaching tips & learning objectives

Learning objectives

Solve quadratic equations by completing the square.
Express integer and radical solutions in exact form.
Match solution pairs with a color-coded answer bank.

Teaching tips

Identify any rearrangement or leading-coefficient step before completing the square.
Ask students to retain their working and check solutions in the original equation.
Use the answer bank to select colors after solving.

Skills covered

Completing the square — students transform and solve twelve quadratics, including problems with leading coefficients that must be factored out first.
Working with radical solutions — answers include exact forms such as x = 4 ± 2√10 and x = -9 ± 5√3 that students must simplify correctly to match the bank.
Self-checking work — students check each solution against the color-coded answer bank before coloring the picture.

Good to know

Questions teachers ask about this resource

What kinds of solutions do the equations produce?

A mix — some problems give integer pairs like x = 2, 4 or x = 8, 10, while others require exact radical answers such as x = 4 ± √11 or x = -9 ± 5√3, so students practice both clean and irrational results.

Do all the problems start in the same form?

No — some begin with the constant on the right (x² - 6x = -8), some are in standard form, and several carry a leading coefficient, like 4x² - 48x + 104 = 0, that must be divided out before completing the square.

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Curriculum

Standards, concepts & topics

Standards

HSA-REI.B.4 — Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. b. 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.

Core concepts

Quadratic equations
Completing the square
Radical solutions
Color-by-number practice

Topics

Completing the square Quadratic equations Color by number Algebra practice Equation solving

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Categories this resource belongs to

9th Grade Math Worksheets 8th Grade Math Worksheets Algebra Worksheets Math Worksheets Popular Math Worksheets High School Worksheets

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