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3.8 Warm Up Write the function in vertex form (by completing the square) and identify the vertex. a. y = x² + 14x + 11 b. y = 2x² + 4x – 5 c. y = x² - 8x + 10

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Lesson 3.8 Quadratic Formula & Discriminant

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Quadratic Formula The quadratic formula!

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Examples 1. 3x 2 +8x=35 3x 2 +8x-35=0 a=3, b=8, c= -35 OR

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2. -2x 2 =-2x-3 -2x 2 +2x+3=0 a=-2, b=2, c= +3

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3. x 2 =6x-10 4. x² + 2x = 4x 5. -6x² + 3x + 2 = 3

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Discriminant: b 2 - 4ac (the number under the square root) The discriminant tells you how many solutions and what type you will have. If the discriminant is: positive - then 2 real solutions negative - then 2 imaginary solutions zero – 1 real solution

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Examples Find the discriminant and give the number and type of solutions. a. 9x 2 +6x+1=0 a=9, b=6, c=1 b 2 -4ac=(6) 2 -4(9)(1) =36-36=0 1 real solution b. 9x 2 +6x-4=0 a=9, b=6, c=-4 b 2 -4ac=(6) 2 -4(9)(-4) =36+144=180 2 real solutions c. 9x 2 +6x+5=0 a=9, b=6, c=5 b 2 -4ac=(6) 2 -4(9)(5) =36-180=-144 2 imaginary solutions

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Try these... How many solutions? Real or Imaginary? 6. 3x² + 2x – 1 = 0 7. -x² + 1 = -5x² + 4x 8. x² - 2x + 1 = 0

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