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1.5 Solving Quadratic Equations by Finding Square Roots

1.5 Solving Quadratic Equations by Finding Square Roots. (p. 32) How do you simplify radicals? What are the steps to rationalize a denominator? What is a conjugate? How many answers will you get when you solve a quadratic equation by finding square roots?

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1.5 Solving Quadratic Equations by Finding Square Roots

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  1. 1.5 Solving Quadratic Equations by Finding Square Roots (p. 32) How do you simplify radicals? What are the steps to rationalize a denominator? What is a conjugate? How many answers will you get when you solve a quadratic equation by finding square roots? Identify the formula h = −16t2 + h0?

  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. Conjugates

  9. Rationalize the denominator of fractions SOLUTION

  10. Guided Practice

  11. 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

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

  13. 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

  14. 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?

  15. How do you simplify radicals? • What are the steps to rationalize a denominator? • What is a conjugate? • How many answers will you get when you solve a quadratic equation by finding square roots? • Identify the formula h = −16t2 + h0?

  16. Assignment p. 35, 4-18 even, 22-32 even, 38, 39

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