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Analyzing Quadratic Equations: Discriminant and Quadratic Formula

Learn how to analyze the discriminant of a quadratic equation to determine the number and type of solutions. Practice solving equations using the quadratic formula. Homework included.

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Analyzing Quadratic Equations: Discriminant and Quadratic Formula

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  1. Do Now Use the standard form of a quadratic equation to find the a, b and c of each equation. ax2 + bx + c = 0 • x2 – 6x + 10 = 0 • 2x2 + 3x + 4 = 0 • x2 – 5x – 7 = 8

  2. 3.4 Using the Quadratic Formula Objective: analyze the discriminant to determine the number and type of solutions

  3. You can analyze the discriminant of a quadratic equation to determine the number and type of solutions of the equation.

  4. Examples: Analyzing the Discriminant Find the discriminant of the quadratic equation and describe the type of solution of the equation. a. x2 – 6x + 10 = 0 b.x2 – 6x + 9 = 0 c. x2 – 6x + 8 = 0

  5. Practice: Analyzing the Discriminant Find the discriminant of the quadratic equation and describe the type of solution of the equation. 1. 4x2 + 8x + 4 = 0 2. ½x2 + x – 1 = 0

  6. Practice: Analyzing the Discriminant Find the discriminant of the quadratic equation and describe the type of solution of the equation. 3. 5x2 = 8x – 13 4. 7x2 – 3x = 6

  7. Practice: Analyzing the Discriminant Find the discriminant of the quadratic equation and describe the type of solution of the equation. 5. 4x2 + 6x = – 9 6. –5x2 + 1 = 6 – 10x

  8. The Quadratic Formula Solve using the quadratic formula. x2 + 3x – 5 = 0

  9. Example: Solve using the quadratic formula. x2 – 6x+9 = 0

  10. Practice solving equations with the quadratic formula. • x2 + 2x – 3 = 0 • 2x2 + 4x – 1 = 0 • 3x2 – 2x – 6 = 0

  11. Homework Section 3.4 Practice A Worksheet

  12. Do Now • Determine the number and type of solutions to the equation x2 + 7x = – 11 • Two real solutions • One real solution • Two imaginary solutions • One imaginary solution

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