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Lesson 8-1 Introducing Quadratic Equations

This lesson introduces quadratic equations and teaches students how to solve them using factoring and completing the square methods. Understand the quadratic equations form (ax2 + bx + c = 0) and apply it to real-world scenarios like gravity affecting height. Practice solving quadratics by isolating x2 and x terms, factoring, and completing the square. Examples and assignments included.

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Lesson 8-1 Introducing Quadratic Equations

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  1. Lesson 8-1Introducing Quadratic Equations Objectives Students will: Solve quadratic equations by factoring and completing the square

  2. Quadratic Equations Form: ax2 + bx + c = 0 Example: 16t2 + v0t – h = 0 v0 = initial velocity; h = height Anything affected by gravity will be quadratic Solving Quadratics x2 & x terms: if Just x2 term: Set equal to zero Factor completely Set factors equal to 0 Can isolate x2 term Square root both sides Remember both roots!!

  3. Understand • Compare and

  4. Example 1Example 2 • 2x2 + 7x = 0 2x2 + 3 = 0

  5. Example 3:

  6. assignment 8-1/345-346/1-35 odd,65-73 o

  7. Try to solve: x2 – 2x – 5 = 0 We need a technique to solve these

  8. Completing the Square • Method: x2 – 2x – 5 = 0 • Move constant term x2 – 2x = 5 • Make front coefficient 1 • 3) Add the square of half the middle x2 – 2x + 1 = 6 • term to both sides • 4) Factor trinomial as perfect square (x – 1)2 = 6 • 5) Square root both sides x – 1 = • 6) Solve for x x = 1 This means x=1 is the axis of symmetry

  9. Example 3 1) 2) 3) 4) 5) 6)

  10. Example 4 1) 2) 3) 4) 5) or 6)

  11. Assignment 8-1/345-346/ 44-52,58-59 58) 44) 46) 48) 50) 52)

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