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2-6 The Quadratic Formula Warm Up Write each function in standard form. 1. f(x) = (x – 4)2 + 3 2. g(x) = 2(x + 6)2 – 11 Evaluate b2 – 4ac for the given values of the valuables. 3. a = 2, b = 7, c = 5 Holt McDougal Algebra 2 4. a = 1, b = 3, c = –3 2-6 The Quadratic Formula Objectives Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant. Vocabulary discriminant Holt McDougal Algebra 2 2-6 The Quadratic Formula You can use the Quadratic Formula to solve any quadratic equation that is written in standard form, including equations with real solutions or complex solutions. Remember that all quadratics are symmetric about the _____________________ Holt McDougal Algebra 2 2-6 The Quadratic Formula Example 1: Quadratic Functions Find the zeros using the Quadratic Formula. f(x)= 2x2 – 16x + 27 Holt McDougal Algebra 2 f(x) = 4x2 + 3x + 2 2-6 The Quadratic Formula The discriminant is part of the Quadratic Formula that you can use to determine the number of real roots of a quadratic equation. Holt McDougal Algebra 2 2-6 The Quadratic Formula Example 3: Analyzing Quadratic Equations by Using the Discriminant Find the type and number of solutions for the equation. x2 + 36 = 12x Holt McDougal Algebra 2 x2 + 40 = 12x x2 + 30 = 12x 2-6 The Quadratic Formula The graph shows related functions. Notice that the number of real solutions for the equation can be changed by changing the value of the constant c. Holt McDougal Algebra 2 2-6 The Quadratic Formula Example 4: Sports Application An athlete on a track team throws a shot put. The height y of the shot put in feet t seconds after it is thrown is modeled by y = –16t2 + 24.6t + 6.5. The horizontal distance x in between the athlete and the shot put is modeled by x = 29.3t. To the nearest foot, how far does the shot put land from the athlete? Holt McDougal Algebra 2 2-6 The Quadratic Formula Properties of Solving Quadratic Equations Holt McDougal Algebra 2 2-6 The Quadratic Formula Properties of Solving Quadratic Equations Holt McDougal Algebra 2 2-6 The Quadratic Formula Helpful Hint No matter which method you use to solve a quadratic equation, you should get the same answer. HW pg 105 18-58e, 61-64 Holt McDougal Algebra 2