Unit 3: Quadratics, Powers and Polynomials
- I. Essential Purpose
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In this unit, students will be introduced to graphing and solving quadratic functions. Students will determine how to simplify powers and polynomial expressions. Topics include: addition, subtraction, multiplication, and factoring of polynomials; graphing and solving quadratic equations; and operations with powers: multiplication, division, power to a power, negative and zero exponents.
- II. State/Local Standards
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2.1.11.A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms).
2.5.11.C Present mathematical procedures an results clearly, systematically, succinctly and correctly.
2.8.11.O Determine domain and range of relation, given a graph or set of ordered pairs.
2.8.11.N Solve linear, quadratic and exponential equations both symbolically and graphically.
2.8.11.R Create and interpret functional models.
2.8.11.S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic).
- III. Essential Questions
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- How does the graph of a quadratic relate to the solutions of a quadratic?
- How do you simplify algebraic expressions?
- IV. Unit Questions
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- V. Essential Content
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- Graph quadratic functions. Be able to identify the vertex, line of symmetry, domain, and range.
- Solve quadratic equations by graphing, quadratic formula, and the quadratic formula program.
- Perform operations with polynomials: addition, subtractions, multiplication, and factoring.
- Simplify expressions involving powers; multiplication, division, negative and zero exponents, powers to powers.
- VI. Essential Skills
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Students will be able to add, subtract, and multiply polynomials.
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Students will be able to factor polynomial expressions by taking out the Greatest Common Factor and/or by factoring quadratic binomials and trinomials.
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Students will be able to graph quadratic functions, determine the vertex, line of symmetry, domain, and range.
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Students will also be able to find points on the graph, specifically the x-intercept(s) and y-intercept.
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Students will be able to solve quadratics by graphing and by the quadratic formula.
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Students will be able to perform multiplication and division of expressions with powers.
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Students will be able to raise a power to a power.
- Students will be able to simplify powers containing negative and zero exponents.
- VII. Resources
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Templates
Toolkits
Additional Resources
- VIII. Summative Assessment/Performance Task
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Tests, Quizzes, and Reviews
Benchmarks and Reviews