CCSS.Math.Content.HSA-REI.B.4b
The Standard
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.
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 choose a suitable method based on the equation’s form, then solve for all roots. They recognize a negative discriminant and write the resulting complex roots as a ± bi.
What Mastery Looks Like
- Students choose an efficient method from the equation’s form and find every solution accurately. They check solutions and use the discriminant to distinguish two real roots, one repeated root, or two complex roots.
Common Misconceptions
- Students forget the ± when taking square roots, fail to set each factor equal to zero, or make sign errors with b. They may call a negative discriminant “no solution” instead of writing complex solutions.
How to Assess It
- Exit ticket: Solve x² + 4x + 8 = 0 with the quadratic formula, write both solutions as a ± bi, and interpret the discriminant.
Lesson moves
Ways to Teach It
Use algebra tiles to complete the square for x² + 6x = 7, then read and verify both solutions.
Compare x² = 36 and (x − 4)² = 36, then explain why each has two solutions and where ± enters.
Run a card sort where students match quadratic equations to factoring, square roots, completing the square, or the quadratic formula before solving.
Model a tossed ball with h(t) = −5t² + 20t + 1, solve h = 0, and interpret the positive root.
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Printable HSA-REI.B.4b Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-REI.B.4b, with an answer key for the teacher on its own page. No account needed.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSN-CN.A.1
Knowing i² = -1 and a + bi notation lets students express quadratic formula results with negative discriminants.
- CCSS.Math.Content.HSA-SSE.B.3a
Factoring quadratics to identify zeros carries directly into solving quadratic equations by factoring when that form is appropriate.
- CCSS.Math.Content.HSA-REI.B.4a
Completing the square to reach (x-p)²=q supports using square roots and the quadratic formula to solve general quadratics.
What This Unlocks
Mastery here sets students up for these next.
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Related Standards
- CCSS.Math.Content.HSA-REI.B.4
Solve quadratic equations in one variable.
- CCSS.Math.Content.HSF-IF.C.8a
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in ...
- CCSS.Math.Content.HSN-CN.C.7
Solve quadratic equations with real coefficients that have complex solutions.
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