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Quadratic Formula: Solve Equations by Completing the Square

Learn how to solve quadratic equations using the quadratic formula and determine the number of solutions using the discriminant. Practice and master these skills with examples, guided practice, and homework assignments.

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Quadratic Formula: Solve Equations by Completing the Square

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  1. 5 minutes Warm-Up Solve by completing the square. 1) x2 – 10x + 23 = 0 2) 5x2 – 10x - 10 = 0

  2. 13.4.1 The Quadratic Formula Objectives: Students will use the quadratic formula to solve quadratic equations. Determine the number of solutions by utilizing the discriminant. Mastery is 80% or better on 5-min check and Indy work.

  3. Concept Dev-The Quadratic Formula If ax2 + bx + c = 0, a = 0, then the quadratic formula gives the solutions of the quadratic equation.

  4. Skill Dev-Example 1 Solve using the quadratic formula. 3x2 – 7x + 2 = 0

  5. Example 1 Solve using the quadratic formula. 3x2 – 7x + 2 = 0

  6. Skill Dev- Example 2 Solve using the quadratic formula. -x2 + x + 1 = 0

  7. Example 2 Solve using the quadratic formula. -x2 + x + 1 = 0

  8. Guided-Practice…Boards Solve using the quadratic formula. Approximate the solutions to the nearest tenth. 1) 2x2 – 4x = 5 2) x2 + 5x = -3

  9. Guided- Practice Use the quadratic formula to find the roots of each polynomial. 1) 6x2 – 6 – 5x 2) 6x2 – 6x - 5

  10. Homework HW PDF Online Quad Formula & Disc

  11. 5 minutes Warm-Up Solve using the quadratic formula. 1) x2 = 8x - 16 2) 3x2 – 4x – 2 = 0

  12. 13.4.2 The Quadratic Formula Objectives: To use the quadratic formula to solve quadratic equations To use the discriminant to find the number of solutions for a quadratic equation

  13. The Discriminant The expression under the radical, b2 – 4ac, is called the discriminant. We can use the discriminant to determine the number of solutions b2 – 4ac is positive: two real number solutions b2 – 4ac is zero: one real number solution b2 – 4ac is negative: no real number solutions

  14. Skill Dev - Example 1 Determine the number of real solutions, then solve using the quadratic formula. 4x2 – 7x + 2 = 0 b2 – 4ac = 49 – (4)(4)(2) b2 – 4ac = 17 two real solutions

  15. Guided - Practice Determine the number of real solutions, then solve using the quadratic formula. 1) x2 + 5x = -8 2) 4x2 = 8x - 4 3) 4x2 + 4x = 15

  16. Think..Ink..Share Practice Use the discriminant to determine whether the graph of each quadratic function intersects the x-axis in 0,1, or 2 points. 1) y = 3x2 - 5x + 1 2) f(x) = x2 – 3x + 7 3) y = x2 – 12x + 36

  17. What did you learn? • Students will use the quadratic formula to solve quadratic equations. Determine the number of solutions by utilizing the discriminant. • Mastery is 80% or better on 5-min check and Indy work.

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