1.5 Solving Quadratic Equations by Finding Square Roots

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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?

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How would you solve the equationx2 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

• (agt0 and bgt0)
• Product Property
• 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.

Cant have a tent in the basement!
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Conjugates

•  

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Rationalize the denominator of fractions
SOLUTION
 
 
 
 
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Guided Practice
 
 
 
 
 
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Solving Quadratic Equations

• Solve. 3 - 5x2 -9
• -3 -3
• -5x2 -12
• -5 -5
• x2

• Solve. 3(x-2)221

3 3
(x-2)2 7
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More Examples!
4. Solve.

• Solve. 4x2-642
• 6 6
• 4x248
• 4 4
• x2 12

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Falling Objects!

• Use h -16t2 h0

Height of the object after it has fallen
Objects initial height
of seconds after the object is dropped
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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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• 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?

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