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Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503

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What is a square root? If a number square (b 2 ) = another number (a), then b is the square root of a. Example: If 3 2 = 9, then 3 is the square root of 9

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Some basics… All positive numbers have two square roots The 1 st is a positive square root, or principal square root. The 2 nd is a negative square root Square roots are written with a radical symbol You can show both square roots by using the “plus-minus” symbol ±

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Find the square root of numbers

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Perfect Squares: Numbers whose square roots are integers or quotients of integers.

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Evaluate a Radical Expression

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Quadratic Equations Standard form: ax 2 + bx + c = 0 a is the leading coefficient and cannot be equal to zero. If the value of b were equal to zero, the equation becomes ax 2 + c = 0. We can solve equations is this form by taking the square root of both sides.

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Key Concepts When x 2 = d If d > 0, then x 2 = d has two solutions If d = 0, then x 2 = d has one solution If d < 0, then x 2 = d has no real solution

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Solving quadratics Solve each equation. a. x 2 =4 b. x 2 =5 c. x 2 =0 d. x 2 =-1 x 2 =4 has two solutions, x = 2, x = -2 x 2 =5 has two solutions, x =√5, x =- √5 x 2 =0 has one solution, x = 0 x 2 =-1 has no real solution

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Solve by rewriting equation Solve 3x 2 – 48 = 0 3x 2 – 48 + 48 = 0 + 48 3x 2 = 48 3x 2 / 3 = 48 / 3 x 2 = 16 After taking square root of both sides, x = ± 4

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Equation of a falling object When an object is dropped, the speed with which it falls continues to increase. Ignoring air resistance, its height h can be approximated by the falling object model. h is the height in feet above the ground t is the number of seconds the object has been falling s is the initial height from which the object was dropped

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Application An engineering student is in an “egg dropping contest.” The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking the egg. To the nearest tenth of a second, about how long will it take for the egg’s container to hit the ground? Assume there is no air resistance.

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The question asks to find the time it takes for the container to hit the ground. Initial height (s) = 32 feet Height when its ground (h) = 0 feet Time it takes to hit ground (t) = unknown

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Substitute 0 = -16t 2 + 32 -32 + 0 = -16t 2 + 32 – 32 -32 = -16t 2 -32 / -16 = -16t 2 / -16 2 = t 2 t = √2 seconds or approx. 1.4 seconds

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