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The Quadratic Formula

The Quadratic Formula. Solving Quadratic Equations using the Quadratic Formula. Introducing the QUADRATIC FORMULA. Given a quadratic equation in Standard Form: ax 2 + bx + c = 0 a ≠ 0 The solutions can be found using the coefficients: a, b, and c, and the following formula:.

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The Quadratic Formula

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  1. The Quadratic Formula Solving Quadratic Equations using the Quadratic Formula KM & PP

  2. Introducing the QUADRATIC FORMULA Given a quadratic equation in Standard Form: ax2 + bx + c = 0a ≠ 0 The solutions can be found using the coefficients: a, b, and c, and the following formula: KM & PP

  3. The Quadratic Formula is the QUADRATIC Formula is the DISCRIMINANT KM & PP

  4. Quadratic Formula: The Discriminant Since the Discriminant is under the square root, it will determine the nature of the solutions of the quadratic equation. KM & PP

  5. Positive Discriminant If the Discriminant is positive, ax2 + bx + c = 0has two unequal Real solutions KM & PP

  6. Zero Discriminant If the Discriminant is zero, ax2 + bx + c = 0has one Real solution(a double root) KM & PP

  7. Negative Discriminant If the Discriminant is negative, ax2 + bx + c = 0has NO REAL solutions. Ø KM & PP

  8. Nature of theSolutions Compute the discriminant and describe the nature of the roots. 3x2 – 4x + 5 = 0 a = 3 b = -4 c = 5 negative 3x2 – 4x + 5 = 0 has no Real solutions KM & PP

  9. Nature of theSolutions Compute the discriminant and describe the nature of the roots. 4x2 – 12x + 9 = 0 a = 4 b = -12 c = 9 zero 4x2 – 12x + 9 = 0 has one Real solution (a double root) KM & PP

  10. Nature of theSolutions Compute the discriminant and describe the nature of the roots. 2x2 - 3x - 1 = 0 a = 2 b = -3 c = -1 positive 2x2 – 3x -1 = 0 has two unequal Real solutions. KM & PP

  11. Solve Using the Quadratic Formula clear fractions and put in standard form substitute a, b, and c into the formula KM & PP

  12. Solve Using the Quadratic Formula simplify KM & PP

  13. Solve Using the Quadratic Formula or KM & PP

  14. Solve Using the Quadratic Formula Under construction {(3 +11)/2} KM & PP

  15. Solve Using the Quadratic Formula Under construction {(2 +10) / 2} KM & PP

  16. Solve Using the Quadratic Formula Under construction {-1/5, 3/2} KM & PP

  17. That’s All for Now! KM & PP

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