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NAME _____________________________________________ DATE ____________________________ PERIOD _____________ 9-5 Solving Quadratic Equations by Using the Quadratic Formula To solve the standard form of the quadratic equation, ax2 + bx + c = 0, use the Quadratic Formula. The solutions of ax2 + bx + c = 0, where a ≠ 0, are given by Quadratic Formula b b 2 4ac x= 2a Example 1: Solve x2 +2x = 3by using the Quadratic Formula. b b2 4ac or x = 2a Example 2: Solve x2 – 6x – 2 = 0 by using the Quadratic Formula. Round to the nearest tenth if necessary. NAME _____________________________________________ DATE ____________________________ PERIOD _____________ Exercises Solve each equation by using the Quadratic Formula. Round to the nearest tenth if necessary. 1. x2 – 3x + 2 = 0 2. 16x2 – 8x = -1 3. 3x2 + 2x = 8 NAME _____________________________________________ DATE ____________________________ PERIOD _____________ 9-5 Solving Quadratic Equations by Using the Quadratic Formula The Discriminant In the Quadratic Formula, the expression under the radical sign, b2 – 4ac, is called the discriminant. The discriminant can be used to determine the number of real solutions for a quadratic equation. Case 1: b2 – 4ac < 0 no real solutions Case 2: b2 – 4ac = 0 one real solution Case 3: b2 – 4ac > 0 two real solutions Example: State the value of the discriminant for each equation. Then determine the number of real solutions of the equation. a. 12x2 + 5x = 4 b. 2x2 + 3x = -4 Exercises State the value of the discriminant for each equation. Then determine the number of real solutions of the equation. 1. 3x2 + 2x – 3 = 0 discriminant = ______________ NAME _____________________________________________ DATE ____________________________ PERIOD _____________ Exercises State the value of the discriminant for each equation. Then determine the number of real solutions of the equation. 2. 2x2 – 10x – 9 = 0 discriminant = _______________ 3. 6x2 – 10x + 10 = 0 discriminant = ________________ 4. 9 – 18x + 9x2 = 0 discriminat = __________________ NAME _____________________________________________ DATE ____________________________ PERIOD _____________ 5. 16x2 + 16x + 4 = 0 discriminant = __________________ 6. 3x2 – 18x = -14 discriminant = ____________________ 7. 4x2 - 4x + 4 = 3 discriminant = ____________________