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5.6 Quadratic Formula & Discriminant

5.6 Quadratic Formula & Discriminant. p. 291. Discriminant: b 2 -4ac. The discriminant (a numerical value) that tells you how many solutions and what type you will have. If the discrimant : Is a positive number – 2 real solutions Is a negative number – 2 imaginary solutions

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5.6 Quadratic Formula & Discriminant

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  1. 5.6 Quadratic Formula & Discriminant p. 291

  2. Discriminant: b2-4ac • The discriminant (a numerical value) that tells you how many solutions and what type you will have. • If the discrimant: Is a positive number – 2 real solutions Is a negative number – 2 imaginary solutions Is zero – 1 real solution

  3. Find the discriminant and give the number and type of solutions. 9x2+6x+1=0 a=9, b=6, c=1 b2-4ac=(6)2-4(9)(1) =36-36=0 1 real solution 9x2+6x-4=0 a=9, b=6, c=-4 b2-4ac=(6)2-4(9)(-4) =36+144=180 2 real solutions c. 9x2+6x+5=0 a=9, b=6, c=5 b2-4ac=(6)2-4(9)(5) =36-180=-144 2 imaginary solutions Examples

  4. Quadratic Formula(Yes, it’s the one with the song!) If you take a quadratic equation in standard form (ax2+bx+c=0), and you complete the square, you will get the quadratic formula!

  5. Let’s complete the square to get the quadratic formula • ax2+bx+c=0

  6. When to use the Quadratic Formula(anytime you want) Use the quadratic formula when you can’t factor to solve a quadratic equation. (or when you’re stuck on how to factor the equation.)

  7. Examples • 3x2+8x=35 3x2+8x-35=0 a=3, b=8, c= -35 OR

  8. -2x2=-2x+3 -2x2+2x-3=0 a=-2, b=2, c= -3

  9. Applications • Dropped Object • Thrown or Launched Object h = height t = time in motion h0 = initial height v0 = initial vertical velocity

  10. Applications • A baton twirler tosses a baton into the air. The baton leaves the twirler’s hand 6 feet above the ground and has an initial velocity of 45 feet per second. The twirler catches the baton when it falls back to a height of 5 feet. For how long is the baton in the air?

  11. AssignmentPage 295 problems 4 - 16

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