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10.6 Using the Quadratic Formula

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10.6 – Quadratic Formula Goals / “I can…” Use the quadratic formula when solving quadratic equations Choose an appropriate method for solving a quadratic equation

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10.6 – Quadratic Formula We have used a couple of ways to find the zeros of a quadratic. 1.Graphing 2.Factoring 3.Square roots 4.Completing the square

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y = x 2 – 4x – 5 Solutions are -1 and 5 10.6 – Quadratic Formula How many solutions are there? What are they?

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1. 25x 2 = 16 ANSWER 4 5 4 5 –, 2. 9m 2 = 100 ANSWER 10 3 –, 3 3. 49b 2 + 64 = 0 ANSWER no solution 10.6 – Quadratic Formula Use the Square Root method to solve:

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Example 1 x 2 – 2x – 24 = 0 (x + 4)(x – 6) = 0 x + 4 = 0 x – 6 = 0 x = –4 x = 6 Example 2 x 2 – 8x + 11 = 0 x 2 – 8x + 11 is prime; therefore, another method must be used to solve this equation. 10.6 – Quadratic Formula

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Solve x 2 – 16x = –15 by completing the square. SOLUTION Write original equation. x 2 – 16x = –15 Add, or (– 8) 2, to each side. – 16 2 2 x 2 – 16x + (– 8) 2 = –15 + (– 8) 2 Write left side as the square of a binomial. (x – 8) 2 = –15 + (– 8) 2 Simplify the right side. (x – 8) 2 = 49 10.6 – Quadratic Formula

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However, each one is difficult if the zeros are decimals or fractions. Quadratic Formula The last way to find the zeros is to use the Quadratic Formula.

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10.6 – Quadratic Formula Quadratic formula Quadratic formula KNOW IT!!! LOVE IT!!! MEMORIZE IT (place it in your brain so that it can be recalled at anytime)

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10.6 – Quadratic Formula The letters a, b, and c refer to the letters in the quadratic equation: ax + bx + c = 0. 2

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10.6 – Quadratic Formula EXAMPLE: 7x – 2x – 8 = 0 Write down the letters: a = 7, b = -2, c = -8 2

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10.6 – Quadratic Formula Substitute the letters into the equation. = =1.22, - 0.94

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10.6 – Quadratic Formula

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x 2 – 8x – 17 = 0 a = 1 b = –8 c = –17

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a =b =c =110-7 10.6 – Quadratic Formula

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How do you know which way to solve a quadratic equation? Graphing – calculator handy (easy x – int) y = x + 3 2

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10.6 – Quadratic Formula How do you know which way to solve a quadratic equation? Square roots – No bx term to solve x – 25 = 0 2

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10.6 – Quadratic Formula How do you know which way to solve a quadratic equation? Factoring – If it is easily factored x + x – 42 = 0 2

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10.6 – Quadratic Formula How do you know which way to solve a quadratic equation? Completing the square – Use if the x term is 1, but you CANNOT factor easily. x + 8x = 48 2 2

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10.6 – Quadratic Formula How do you know which way to solve a quadratic equation? Quadratic Formula – Use if the equation can’t be factored / easily factored. 7x – 2x – 8 = 0 2

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