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Interpret the Discriminant (10.7) To Solve Quadratic Equations in the form ax2 + bx + c = 0, where b 0 we can use the Quadratic Formula: b b 4ac 2a 2 x **Note: Be sure to put the equation in standard form first: ax2 + bx + c = 0 The b2 – (4ac) is called the discriminant The value of the discriminant can be used to determine the number of solutions We learned that a quadratic equation can have a different number of solutions: 2 Solutions 2 points of intersection 1 Solution 1 point of intersection No Solution No point of intersection b2 – (4ac) is Positive Number b2 – (4ac) is 0 b2 – (4ac) is Negative Number 1 Tell whether the equation has two solutions, one solution, or no solution. Ex. 2x2 + 6x + 5 = 0 a = _____ b = _____ c = _____ b2 – (4ac) = _______________________ = ______ number of solutions: __________________ Ex. x2 + 4x + 3 = 0 a = _____ b = _____ c = _____ b2 – (4ac) = _______________________ = ______ number of solutions: __________________ Ex. 4x2 – 12x + 9 = 0 a = _____ b = _____ c = _____ b2 – (4ac) = _______________________ = ______ number of solutions: __________________ Ex. 3x2 – 7 = 2x a = _____ b = _____ c = _____ b2 – (4ac) = _______________________ = ______ number of solutions: __________________ 2
