5.3 Solving Quadratic Equations by Finding Square Roots

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5.3 Solving Quadratic Equations by Finding
Square Roots

• Goals 1. Solve quadratic equations by finding
• square roots
• 2. using quadratic models in real life

For what purpose would you use the product or
quotient properties of square roots when solving
quadratic equations using square roots?
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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!
• Just multiply the top bottom of the fraction by
  the radical to rationalize the denominator.

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Examples

• 1.
• 2.

Cant have a radical in the denominator!
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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?