CCSS.Math.Content.HSA-SSE.B.3b
The Standard
Complete the square in a quadratic expression to reveal the maximum or minimum value 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 in vertex form by creating a perfect-square trinomial. They use that form to find the function's maximum or minimum value and where it occurs.
What Mastery Looks Like
- Given a quadratic expression, students factor out the leading coefficient when needed and rewrite the expression as a(x − h)² + k. They identify k as the maximum or minimum and h as the input where it occurs.
Common Misconceptions
- Students may halve the wrong coefficient after factoring out the leading coefficient, or forget to square the halved value. They may change the expression's value, confuse the vertex coordinates, or reverse maximum and minimum based on the leading coefficient's sign.
How to Assess It
- Exit ticket: Rewrite 2x² + 8x - 3 in vertex form. State the minimum value and the x-value where it occurs.
Lesson moves
Ways to Teach It
Give pairs algebra tiles to build x² + 6x + 2, complete the square physically, and record (x + 3)² − 7.
Ask, "How does 3(x − 4)² − 5 show the lowest point without graphing?" Students write a two-sentence explanation.
Run a matching-card game with standard-form expressions, vertex forms, and maximum or minimum statements; students justify each set before keeping it.
Model a kicked ball with h(t) = −16t² + 48t + 5, then complete the square to find its greatest height.
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Printable HSA-SSE.B.3b Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-SSE.B.3b, 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
Seeing quadratic structure supports rewriting ax²+bx+c into vertex form, where the square term reveals the maximum or minimum.
- CCSS.Math.Content.HSA-SSE.B.3
Choosing equivalent forms supports completing the square, where rewriting a quadratic reveals its vertex and maximum or minimum.
What This Unlocks
Mastery here sets students up for these next.
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Related Standards
- CCSS.Math.Content.HSF-IF.C.7a
Graph linear and quadratic functions and show intercepts, maxima, and minima.
- CCSS.Math.Content.HSA-REI.B.4b
Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to ...
- CCSS.Math.Content.HSA-SSE.B.3a
Factor a quadratic expression to reveal the zeros of the function it defines.
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