Solving quadratics with square roots

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Solving quadratics with square roots

  1. 1. 4.5 Solving Quadratic Equations by Finding Square Roots (p. 250-253)
  2. 2. How would you solve the equation: x2 = 4 (take the square root of each side!) x =4 2 x = 4 x = 2 or - 2 * 2 * Remember, the square root of a positive # has 2 answers! (one + and one -)
  3. 3. Radical 3 Radical sign Radicand
  4. 4. Properties of Square Roots (a>0 and b>0) 1. Product Property – 2. Quotient Property- ab = a * b a a = b b Example: 40 = 4 *10 = 4 * 10 = 2 10 Example: 3 3 3 = = 4 2 4
  5. 5. Examples 1. 2. 500 = 100 * 5 = 100 * 5 = 10 5 3 12 * 6 = 3 12 * 6 = 3 72 = 3 36 * 2 = 3 * 6 2 = 18 2 3. 25 9 25 = 9 5 = 3
  6. 6. Rationalizing the Denominator You CANNOT leave a radical in the denominator of a fraction! (the numerator is OK) Just multiply the top & bottom of the fraction by the radical to “rationalize” the denominator.
  7. 7. More Examples! 1. 25 3 25 = 3 5 * 3 = 3 * 3 = 5 3 9 = 5 3 3 Can’t have a tent in the basement! 2. 2 11 2 = 11 * 11 22 = * 11 121 22 = 11
  8. 8. Solving Quadratic Equations 1. Solve. 3 - 5x2 = -9 -3 -3 -5x2 = -12 -5 -5 x2 = 12 5 12 x = 5 2 2. Solve. 3(x-2)2=21 3 3 (x-2)2 = 7 ( x − 2) 2 = ± 7 x−2= ± 7 x = 2± 7 12 12 * 5 60 4 *15 ± 2 15 x= = = = = 5 5 5 5*5 25
  9. 9. More Examples! 3. Solve. 4x -6=42 +6 +6 4x2=48 4 4 x2 = 12 x 2 = ± 12 2 x = ± 4 * 3 = ±2 3 1 5 4. Solve. ( x − 4) 2 = 6 ( x − 4) 2 = 30 ( x − 4) 2 = ± 30 x − 4 = ± 30 x = 4 ± 30
  10. 10. Falling Objects! • Use h = -16t2 + h0 Height of the object after it has fallen # of seconds after the object is dropped Object’s initial height
  11. 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? h = −16t 2 + h0 0 = −16t + 1450 2 − 1450 = −16t 90.625 = t 2 2 90.625 = t 2 t ≈ 9.52 seconds

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