Solving Equations y ax2 c

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Solving Equationsy ax2 c
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Warm-Up

• 1)
• 2)
• 3)

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Falling Bodies

• The equation for falling objects is
• y -16x2 s (s is the initial height)
• Another way to solve.
• You are standing on a balcony 12 feet above the
  ground and you drop a key to your friend. How
  long did it take the key the reach the ground?
• y -16x2 12
• y -16x2 12
• 0 -16x2 12

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Continue solving

• 0 -16x2 12
• -12 -12 (subtract 12)
• -12 -16x2
  
• -16 -16 (divide by -16)
• .75 x2
• .866 x (square root both
  sides)

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Vocabulary and Symbols

• Square Root inverse function for a
  square (x2)
• Plus or Minus used to write two
  answers in one

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Steps

• 1) Get x2 or (x a)2 by itself
• 2) Square root both sides to get rid of the
  square
• 3) Solve for x
• Watch Out! The square root of a negative number
  is imaginary.

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Examples
3x2 150 282
(x 3)2 4 12
150 150
4 4
3x2 432
(x 3)2 16
3 3
x2 144
x 3 4 OR x 3 -4
x 7 OR x -1
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One More Example
-2(x 4)2 10 3
-10 -10
Subtract 10
-2(x 4)2 -7
Divide by -2
-2 -2
(x 4)2 3.5
Square Root both Sides
x 4 1.87 0R x 4 -1.87
Subtract 4
x -2.13 OR x -5.87
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Homework!

• Homework Packet Section 4.5
• Pages 64-65
• 1-6, 13-18, 22-25, 32, 33, 36