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Quadratic Formula and the Discriminant

Quadratic Formula and the Discriminant. Essential Questions. How do I use the QUADRATIC FORMULA to solve equations? How do I use the DISCRIMINANT to determine the # of solutions and the factorability for a quadratic equation?. Warm Up. Evaluate each expression. 1) 6 2 – 4(1)(3)

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Quadratic Formula and the Discriminant

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  1. Quadratic Formula and the Discriminant

  2. Essential Questions • How do I use the QUADRATIC FORMULA to solve equations? • How do I use the DISCRIMINANT to determine the # of solutions and the factorability for a quadratic equation?

  3. Warm Up • Evaluate each expression. • 1) 62 – 4(1)(3) • 2) 22 – 4(1)(-3) • 3) • Answers: 24, 16, -1

  4. I will learn to… 10.5 The Quadratic Formula • Use the quadratic formula to find solutions to quadratic equations. • Evaluate the discriminant to determine how many real roots a quadratic equation has (how many solutions there will be).

  5. Vocabulary 10.5 The Quadratic Formula Quadratic Formula: formula used to solve a quadratic equation. Always works! Normally used when you CANNOT factor. Discriminant: expression from the quadratic formula that helps you determine how many real solutions there will be in the quadratic equation. If D < 0 : No Real Solutions If D = 0: Exactly One Real Solution If D > 0: Two Real Solutions

  6. –b b2 – 4ac x = 2a Rules and Properties 10.5 The Quadratic Formula The Quadratic Formula For ax2 + bx + c = 0, where a 0: b2 – 4ac The Discriminant:

  7. –b b2 – 4ac x = 2a Example 1 • Solve using the quadratic formula. 2x2 + 5x + 1 = 0 a = 2, b = 5, c = 1 Plug in!!

  8. Example 2 Solve:3x2 + 2x – 4 = 0 • Can you factor it? • NO • Use the quadratic formula! • A: 3 B: 2 C: -4

  9. Example 2 Continued A: 3 B: 2 C: -4

  10. –5  52 – 4(1)(–8) x = = –5  57 2(1) 2 Example 3Solve using Quad. Formula x2 + 5x – 8 = 0 (this can’t factor!!) a = 1, b = 5, c = –8

  11. You Try • Solve using the quadratic formula. 3x2 – 4x – 2 = 0 a = 3, b = -4, c = -2

  12. “You Try” Continueda = 3, b = -4, c = -2

  13. Ex. 4) Find the # of real solutions. • Remember use the discriminant, b2 – 4ac. • 3x2 – 2x + 1 = 0 • (-2)2 – 4(3)(1) • 4 – 12 • -8 • There are NO real solutions! • By finding the discriminant FIRST ALWAYS, you can save yourself some time if its not workable! • And if you DO discover there are some solutions, you have just already completed part of the Q.F.!  So, you didn’t waste time here either.

  14. More with a +Discriminant • If the discriminant is a perfect square then the equation is factorable! • Don’t use the quadratic formula if you can factor…it is a waste of time. • Ex. If D = 49 you can factor to solve. • Ex. If D = 48 you can only use Q.F.

  15. Think About It • What part of the Q.F. is the discriminant? • The part under the radical!!

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