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
What this standard means
Students need to factor quadratic expressions and connect the factors to the x-values where the related function equals zero. They should see that if a quadratic is written as (x - 3)(x + 2), then the zeros are 3 and -2, and those are also the x-intercepts on a graph.
Mastery means students can choose a factoring method, check by multiplying, and explain what each factor says about the graph or situation. Common trouble spots are sign errors, factoring when the leading coefficient is not 1, and forgetting that zeros come from setting each factor equal to zero.
Ways to teach it
- Give students algebra tiles to build x^2 + 5x + 6, rearrange into a rectangle, then write the factors and zeros.
- Ask students to explain why (x - 4)(x + 1) shows the graph crosses the x-axis at 4 and -1.
- Use a three-question exit ticket: factor one trinomial, find its zeros, and match it to the correct graph.
- Use a projectile height equation and have students factor it to find when the object is on the ground.
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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
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