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
What this standard means
Students need to rewrite a quadratic from standard form into vertex form by completing the square. They should connect the rewritten form to the graph, especially the vertex, axis of symmetry, and whether the function has a maximum or minimum.
Mastery means students can handle expressions like x^2 + 8x + 3 and 2x^2 - 12x + 5, explain the vertex from the form, and state the max or min value. Common snags are forgetting to factor out a leading coefficient, changing the expression’s value, and mixing up the x-value with the output value.
Ways to teach it
- Hands-on activity: Use algebra tiles or printed square diagrams to build x^2 + 6x, add the missing square, and write vertex form.
- Prompt: Explain why x^2 - 10x + 7 has a minimum, then find it by completing the square.
- Quick assessment: Give 3x^2 + 12x - 5 and ask for vertex form, vertex, and minimum value on an exit ticket.
- Real-world connection: Model a thrown ball with h(t) = -16t^2 + 48t + 6 and find its maximum height.
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Graph linear and quadratic functions and show intercepts, maxima, and minima.
- CCSS.Math.Content.HSA-REI.B.4b
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- CCSS.Math.Content.HSF-IF.C.8a
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- CCSS.Math.Content.HSA-SSE.B.3a
Factor a quadratic expression to reveal the zeros of the function it defines.