5.6 Quadratic Formula

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5.6 Quadratic Formula Discriminant

• p. 291

How do you solve a quadratic equation if you
cannot solve it by factoring, square roots or
completing the square? Is there a fast way to
decide?
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Discriminant b2-4ac

• The discriminant tells you how many solutions and
  what type you will have.
• If the discrim Is positive 2 real solutions
• Is negative 2 imaginary
• solutions
• Is zero 1 real solution

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Examples

• 9x26x-40
• a9, b6, c-4
• b2-4ac(6)2-4(9)(-4)
• 36144180
• 2 real solutions
• c. 9x26x50
• a9, b6, c5
• b2-4ac(6)2-4(9)(5)
• 36-180-144
• 2 imaginary solutions

• Find the discriminant and give the number and
  type of solutions.
• 9x26x10
• a9, b6, c1
• b2-4ac(6)2-4(9)(1)
• 36-360
• 1 real solution

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Quadratic Formula(Yes, its the one with the
song!)

• If you take a quadratic equation in standard form
  (ax2bxc0), and you complete the square, you
  will get the quadratic formula!

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When to use the Quadratic Formula

• Use the quadratic formula when you cant factor
  to solve a quadratic equation.
• (or when youre stuck on how to factor the
  equation.)

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Examples

• 3x28x35
• 3x28x-350
• a3, b8, c -35

OR
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• -2x2-2x3
• -2x22x-30
• a-2, b2, c -3

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Assignment
Page 295, 18-72 every third problem, skip 54