CCSS.Math.Content.HSA-REI.B.4a
The Standard
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.
Common Core State Standards for Mathematics · Solve equations and inequalities in one variable
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn a general quadratic equation into a perfect-square equation by dividing, rearranging, and adding the same term to both sides. They then solve symbolically to produce the quadratic formula.
What Mastery Looks Like
- Students correctly divide by the leading coefficient, build a perfect-square trinomial, and preserve equality at each step. They can continue with square roots and simplify the result into the quadratic formula.
Common Misconceptions
- Students may add a term to only one side, forget to divide every term by a, or use half of b instead of half its coefficient after division. They may also lose the plus or minus sign when taking square roots.
How to Assess It
- Give students ax^2 + bx + c = 0 and ask them to complete the square until x is isolated, then simplify to the quadratic formula.
Lesson moves
Ways to Teach It
Use algebra tiles to model x^2 + 6x + 5 = 0, then add pieces to build a perfect square on both sides.
Ask students to explain in writing why adding the same square-building term to both sides keeps the solution set unchanged.
Run a card sort matching quadratic equations, completed-square forms, and solution sets, including examples with leading coefficients other than one.
Rewrite a projectile height equation by completing the square, then identify its maximum height and the time when it occurs.
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Printable HSA-REI.B.4a Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-REI.B.4a, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSA-SSE.A.2
Recognizing quadratic structure supports rewriting ax²+bx+c as a perfect-square expression when completing the square.
- CCSS.Math.Content.8.EE.A.2
Solving the completed-square form and deriving the formula require taking square roots of squared expressions and interpreting both solutions.
- CCSS.Math.Content.HSA-REI.B.3
Completing the square and deriving the formula require fluent equivalent equation moves with variables and literal coefficients.
What This Unlocks
Mastery here sets students up for these next.
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Related Standards
- CCSS.Math.Content.7.EE.B.4a
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these form...
- CCSS.Math.Content.6.EE.B.7
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative r...
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