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Mastering Quadratic Equations: Finding Square Roots and Rationalizing Denominators

This comprehensive guide covers solving quadratic equations by finding square roots, emphasizing the importance of extracting both positive and negative solutions. Learn the properties of square roots, including product and quotient rules, along with practical examples. The text addresses rationalizing denominators to avoid radicals in fractions, ensuring clarity in mathematical representation. Additionally, it explores real-world applications, such as calculating fall times for objects, using important equations. Ideal for students and anyone looking to strengthen their understanding of quadratic equations.

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Mastering Quadratic Equations: Finding Square Roots and Rationalizing Denominators

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  1. 5.3 Solving Quadratic Equations by Finding Square Roots (p. 264) By: L. Keali’i Alicea

  2. How would you solve the equation:x2 = 4(take the square root of each side!) * Remember, the square root of a positive # has 2 answers! (one + and one -)

  3. Radical Radical sign Radicand

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

  5. Examples 1. 2. 3.

  6. 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.

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

  8. Solving Quadratic Equations • Solve. 3(x-2)2=21 • Solve. 3 - 5x2 = -9 -3 -3 -5x2 = -12 -5 -5 x2 = 3 3 (x-2)2 = 7

  9. More Examples! 4. Solve. • Solve. 4x2-6=42 +6 +6 4x2=48 4 4 x2 = 12

  10. Falling Objects! • Use h = -16t2 + h0 Height of the object after it has fallen Object’s initial height # of seconds after the object is dropped

  11. 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?

  12. Assignment

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