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Notes for Lesson 9-9: The Quadratic Formula and the Discriminant 9-9.1&2 – Using the Quadratic Formula Last lesson we solved quadratic equation by completing the square. If we took the standard form of a quadratic and solved it by completing the square, we would have solved it for x. That would give us a formula to use for and quadratic equation. That formula is : X b b 2 4ac where a, b and c come from the quadratic. 2a Examples: Solve using the quadratic formula. 2 x 3x 5 0 A 2, B 3, C 5 2 3 32 4(2)(5) X 2(2) 3 9 40 4 3 49 X 4 3 7 X 4 5 X or1 2 X 2x x2 3 0 x 2 2x 3 A 1, B 2, C 3 (2) (2) 4(1)(3) 2(1) 2 X 2 4 12 2 2 16 X 2 24 X 2 X 3or 1 X x2 2x 4 0 A 1, B 2, C 4 X (2) (2) 2 4(1)(4) 2(1) 2 4 16 2 2 20 X 2 X 9-9.3 – Using the Discriminant Vocabulary: Discriminant – the b 2 4ac in the quadratic formula that tells the number of solutions The discriminant can be use to tell how many solutions there will be to a quadratic equation. If b 2 4ac >0 then there will be 2 solutions because there are 2 square roots If b 2 4ac =0 then there will be one solution because there is only 1 square root of zero If b 2 4ac <0 then there will be no solution because negative numbers have no square roots Examples: Find the number of solutions for each equation using the discriminant 3 x 2 10 x 2 0 10 2 4(3)(2) 100 24 76 2 solutions Do Practice B #’s 2 – 12 even 9x 2 6x 1 x2 x 1 0 (6) 2 4(9)(1) 36 36 (1) 2 4(1)(1) 1 4 0 3 1 solution No Solutions