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Math · Algebra 1 · Unit 8

Unit 8: Quadratic Equations

Students interpret, write, and solve quadratic equations algebraically using factoring, completing the square, and the quadratic formula, and use vertex form to find maximum and minimum values.

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Unit
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Concept
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Practice
Set 1
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Set 2
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Advanced
Set 1
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Set 2
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What this unit covers

A Finding Unknown Inputs · 2 lessons
Goals
  • Write quadratic equations, and reason about their solutions in terms of a situation.
Lessons
  1. Finding Unknown Inputs
  2. When and Why Do We Write Quadratic Equations?
B Solving Quadratic Equations · 8 lessons
Goals
  • Given a quadratic expression, create an equivalent expression in factored form.
  • Use factored form and the zero product property to solve quadratic equations.
Lessons
  1. Solving Quadratic Equations by Reasoning
  2. Solving Quadratic Equations with the Zero Product Property
  3. How Many Solutions?
  4. Rewriting Quadratic Expressions in Factored Form (Part 1)
  5. Rewriting Quadratic Expressions in Factored Form (Part 2)
  6. Rewriting Quadratic Expressions in Factored Form (Part 3)
  7. Solving Quadratic Equations by Using Factored Form
  8. Rewriting Quadratic Expressions in Factored Form (Part 4)
C Completing the Square · 5 lessons
Goals
  • Comprehend that the “plus-minus” symbol is used to represent both square roots of a number and that the square root notation expresses only the positive square root.
  • Solve quadratic equations by rearranging terms and completing the square.
Lessons
  1. What Are Perfect Squares?
  2. Completing the Square (Part 1)
  3. Completing the Square (Part 2)
  4. Completing the Square (Part 3)
  5. Quadratic Equations with Irrational Solutions
D The Quadratic Formula · 6 lessons
Goals
  • Explain whether the products or sums of combinations of rational and irrational numbers are rational or irrational.
  • Use the quadratic formula to solve quadratic equations.
Lessons
  1. The Quadratic Formula
  2. Applying the Quadratic Formula (Part 1)
  3. Applying the Quadratic Formula (Part 2) (Optional)
  4. Deriving the Quadratic Formula
  5. Rational and Irrational Solutions
  6. Sums and Products of Rational and Irrational Numbers
E Vertex Form Revisited · 2 lessons
Goals
  • Rewrite a quadratic expression in vertex form to identify the maximum or minimum value of the function that the expression defines.
Lessons
  1. Rewriting Quadratic Expressions in Vertex Form
  2. Using Quadratic Expressions in Vertex Form to Solve Problems
F Let's Put It to Work · 1 lesson
Lessons
  1. Using Quadratic Equations to Model Situations and Solve Problems
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Adapted from the Illustrative Mathematics curriculum (v.360), licensed CC BY-NC 4.0. © Illustrative Mathematics.