CCSS.Math.Content.HSA-REI.B.4
The Standard
Solve quadratic equations in one variable.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve quadratic equations by factoring, taking square roots, completing the square, or using the quadratic formula. They choose a suitable method, find all real or complex solutions, and check their results.
What Mastery Looks Like
- Students select an efficient method based on the equation’s form and find every solution. They can verify solutions by substitution and use the discriminant to predict the number and type of solutions.
Common Misconceptions
- Students often forget the plus-or-minus sign when taking square roots. They may use the zero-product property before setting the equation equal to zero, lose a root by dividing by a variable, or make sign errors in the quadratic formula.
How to Assess It
- Give this exit ticket: Solve 2x² + 5x - 3 = 0, name your method, and verify both solutions in the original equation.
Lesson moves
Ways to Teach It
Use algebra tiles to build x² + 5x + 6, form a rectangle, and read the factors and roots.
Ask students to compare factoring and the quadratic formula for 2x² + 7x + 3 = 0, then defend the faster method.
Run a card sort matching quadratic equations, solution methods, discriminants, and solution sets.
Model a tossed ball with h(t) = -16t² + 32t + 5, solve for ground time, and reject the negative root.
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Printable HSA-REI.B.4 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-REI.B.4, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSA-SSE.B.3a
Factoring quadratics to find zeros supports solving quadratic equations by using the zero product property.
- CCSS.Math.Content.HSA-SSE.A.2
Recognizing expression structure supports factoring, completing the square, and choosing efficient forms when solving quadratic equations.
- CCSS.Math.Content.8.EE.A.2
Solving quadratics often requires using square roots and recognizing irrational roots, extending the simpler x² = p cases.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSA-REI.C.7
Solving a linear-quadratic system often reduces by substitution to a one-variable quadratic equation whose roots give intersection points.
- CCSS.Math.Content.HSN-CN.C.7
Quadratic solving methods like factoring, completing the square, and the formula carry over when roots become nonreal complex numbers.
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