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Essential Questions: What is the quadratic formula? Why is it useful?

10-6: Using the Quadratic Formula Sometimes you’ll run into a quadratic expression that cannot be factored. Example:x 2 + 10x + 4 = 0 There is no combination of numbers that multiplies to get 4 and adds to 10. Yet, there are real numbers that exist for x to make that a true statement. There exists a formula that allows you to find the solutions for any quadratic equation, called the QUADRATIC FORMULA

10-6: Using the Quadratic Formula A quadratic equation written in standard form ax 2 + bx + c = 0 can be solved with the quadratic equation

10-6: Using the Quadratic Formula Empirical verification that the formula works x 2 + 8x + 12 = 0can be factored as (x + 6)(x + 2) = 0meaning x = -6 OR x = -2 a = 1, b = 8, c = 12

10-6: Using the Quadratic Formula Using the quadratic formula to solve a problem that can’t be factored x 2 + 10x + 4 = 0 a = 1, b = 10, c = 4

10-6: Using the Quadratic Formula Another equation that can’t be factored 2x 2 - 6x + 1 = 0 a = 2, b = -6, c = 1

10-6: Using the Quadratic Formula Assignment Worksheet 10-6 Problems 1 – 29, odds Round answers to the nearest hundredth (2 decimal points)

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