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5.3 Solving Quadratic Equations by Finding Square Roots (p. 264)

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How would you solve the equation: x 2 = 4 (take the square root of each side!) * Remember, the square root of a positive # has 2 answers! (one + and one -)

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Radical Radical sign Radicand

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Properties of Square Roots (a>0 and b>0) 1.Product Property – 2.Quotient Property- Example: Example:

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Examples 1. 2. 3.

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Rationalizing the Denominator You CANNOT leave a radical in the denominator of a fraction! No tents in the basement!!!! (the numerator is OK) Just multiply the top & bottom of the fraction by the radical to “rationalize” the denominator.

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More Examples! 1. 2. Can’t have a tent in the basement!

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Solving Quadratic Equations 1.Solve. 3 - 5x 2 = -9 -3 -3 -5x 2 = -12 -5 -5 x 2 = 2. 2.Solve. 3(x-2) 2 =21 3 3 (x-2) 2 = 7

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More Examples! 3.Solve. 4x 2 -6=42 +6 +6 4x 2 =48 4 4 x 2 = 12 4. Solve.

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Falling Objects! Use h = -16t 2 + h 0 Height of the object after it has fallen # of seconds after the object is dropped Object’s initial height

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Example The tallest building in the USA is in Chicago, Illinois. It is 1450 ft. tall. How long would it take a penny to drop from the top of the building to the ground?

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Quadratic Equations and Complex Numbers

Quadratic Equations and Complex Numbers

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