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Intro: We already know the standard form of a quadratic equation is: y = a x 2 + b x + c

The Quadratic Formula. Intro: We already know the standard form of a quadratic equation is: y = a x 2 + b x + c The coefficients are: a , b, c The variables are: y, x. What it means. The ROOTS (or solutions ) of a polynomial are its x-intercepts

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Intro: We already know the standard form of a quadratic equation is: y = a x 2 + b x + c

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  1. The Quadratic Formula • Intro: We already know the standard form of a quadratic equation is: y = ax2 + bx + c • The coefficients are: a , b, c • The variables are: y, x

  2. What it means • The ROOTS (or solutions) of a polynomial are its x-intercepts • The x-intercepts occur where y = 0.

  3. The Easy Way? • Example: Find the roots: y = x2 + x - 6 • Solution: Factoring: y = (x + 3)(x - 2) • 0 = (x + 3)(x - 2) • The roots are: • x = -3; x = 2

  4. The Formula • After centuries of work, mathematicians realized that as long as you know the coefficients, you can find the roots of the quadratic. Even if it doesn’t factor!

  5. Example

  6. Solution!

  7. Check your answer! Plug in your answers for x. If you’re right, you’ll get y = 0.

  8. Your turn

  9. Tricks of the Trade Remember: All the terms must be on one side BEFORE you use the quadratic formula. • Example: Solve 3m2 - 8 = 10m • Solution:3m2 - 10m - 8 = 0 • a = 3, b = -10, c = -8

  10. Your turn! • Solve: 3x2 = 7 - 2x • Solution: 3x2 + 2x - 7 = 0 • a = 3, b = 2, c = -7

  11. Quadratic Formula • Watch this: http://www.youtube.com/watch?v=jGJrH49Z2ZA

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