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CCSS HSA-REI.B.4.a Worksheets

Algebra 1 · Reasoning with Equations & Inequalities

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, and derive the quadratic formula from this form.

Below are free printable worksheets that support HSA-REI.B.4.a. Print them as PDFs, or generate a fresh one. Every math answer key is computed in code, so it is never wrong.

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Deliver a whole lesson on HSA-REI.B.4.a from a textbook-grade teaching unit, with a hook, worked examples, diagrams, misconceptions, and an exit ticket.

Teaching guide

What students learn

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, and derive the quadratic formula from this form.

Worked example
Rewrite x² + 12x + 31 = 0 in the form (x - p)² = q by completing the square. State p and q.
Answer: p = -6, q = 5
Why: Half the coefficient of x is 12 / 2 = 6, so p = -6. Then q = p² - c = -6² - (31) = 36 - (31) = 5.

Generated and checked in code, so it is correct.

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More Algebra 1 standards: HSA-REI.B.4.b · HSA-APR.A.1 · HSF-LE.A.1.a · HSF-LE.A.1.c · HSF-LE.A.2 · HSN-RN.A.1 · HSN-RN.A.2
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