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negative positive b2 - 4ac zero Summary Number of Real Solutions 2 ? 0 ? 1 ? Find the discriminant and determine the number of real solutions. 1. y = -2x2 + 4x - 4 2. y = -x2 - 6x - 6 3. y = 2x2 - 8x + 8 4. y = x2 - 6x + 13 6. y = -2x2 + 4x - 1 5. y = x2 - 6x + 9 Equation b2 - 4ac Number of Real Zeros (0, 1, or 2) y = x2 + 2x + 0 y = -x2 - 6x -12 Graph no solutions ? x = -2 or 0 ? Solutions Number of RealSolutions 0 (none) ? 2 ? Value ofb2 - 4ac -12 ? 4 ? Is b2 - 4acpositive, negative, or zero? positive ? negative ? y = -x2 - 6x - 13 y = 2x2 - 4x + 2 Graph No solutions ? Solutions x = 1 ? Number of RealSolutions 0(none) ? 1 ? Value ofb2 - 4ac 0 ? -16 ? Is b2 - 4acpositive, negative, or zero? negative ? zero ? y = x2 - 8x + 16 y = -x2 + 8x - 12 Graph Solutions x = 2 or 6 ? x = 4 ? Number of RealSolutions 2 ? 1 ? Value ofb2 - 4ac 16 ? 0 ? Is b2 - 4acpositive, negative, or zero? positive ? zero ? |