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Quadratic and Cubic Functions

Completing the Square (B) WORKSHEET

Suitable for Grades: Algebra I, IM 1
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.

Completing the Square (B) WORKSHEET DESCRIPTION

Throughout this worksheet, students will be writing expressions in ‘completing the square’ form, solving quadratics by completing the square, and taking a look at how this format makes sketching the graphs of quadratics easier.

X squared has a coefficient of 1 for all the questions in section A. The sections build from expressions with two terms to answers that involve fractions.

Next, all the expressions in section B consist of a coefficient of x squared which is greater than 1.

Students are solving quadratics in section C. Knowledge of working with imperfect squares is required here.

Our extension sees learners drawing a graph of an equation from completed square form.

All worksheets are created by the team of experienced teachers at Cazoom Math.

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Frequently Asked Questions

This worksheet is designed for Algebra I and IM 1 students who are working with quadratic and cubic functions. The progressive structure from basic expressions to more complex problems with coefficients greater than 1 makes it well-suited for students at these levels who are building their understanding of quadratic manipulation techniques.