CCSS.Math.Content.HSA-SSE.B.3a
The Standard
Factor a quadratic expression to reveal the zeros of the function it defines.
Common Core State Standards for Mathematics · Write expressions in equivalent forms to solve problems
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite a quadratic expression as a product of linear factors when possible. They use the zero-product property to find where the related graph crosses the x-axis.
What Mastery Looks Like
- A student can factor quadratics with leading coefficients of 1 or greater, including expressions with a common factor. They check by multiplying and correctly identify the corresponding x-intercepts.
Common Misconceptions
- Students often miss a greatest common factor or choose factor signs that produce the wrong middle term. Some treat the factors as zeros instead of setting each factor equal to zero. Others confuse zeros with the y-intercept.
How to Assess It
- Exit ticket: Factor f(x) = 2x² − 7x + 3, state its zeros, and verify one zero by substitution.
Lesson moves
Ways to Teach It
Use algebra tiles to build x² + 5x + 6, arrange a rectangle, and label its side lengths as factors.
Ask students to explain why (x − 4)(x + 2) = 0 gives two possible x-values.
Play Factor Match with cards showing quadratics, factored forms, and zeros, with students racing to form correct sets.
Model a launched ball with h(t) = −5t² + 20t, then factor to find when it is on the ground.
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Printable HSA-SSE.B.3a Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-SSE.B.3a, 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 expression structure supports choosing an appropriate factoring rewrite to expose a quadratic function's zeros.
- CCSS.Math.Content.7.EE.A.1
Factoring quadratics relies on using the distributive property and expression structure first practiced with linear expressions.
- CCSS.Math.Content.HSA-SSE.A.1a
Recognizing terms and factors helps students restructure quadratics and understand why factored form shows zeros.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSA-REI.B.4b
Factoring quadratics to identify zeros carries directly into solving quadratic equations by factoring when that form is appropriate.
- CCSS.Math.Content.HSA-REI.B.4
Factoring quadratics to find zeros supports solving quadratic equations by using the zero product property.
- CCSS.Math.Content.HSF-IF.C.8a
Factoring quadratics to find zeros is directly needed when the target uses factored form to analyze roots and graph features.
Keep exploring
Related Standards
- CCSS.Math.Content.HSA-SSE.B.3b
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- CCSS.Math.Content.HSA-APR.B
Understand the relationship between zeros and factors of polynomials
- CCSS.Math.Content.HSA-APR.B.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial...
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