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Mastering the Quadratic Formula: Solve Equations with Ease

Understand the roots of a polynomial through the quadratic formula. Learn how to find solutions easily by plugging in coefficients and following simple steps. Watch a video tutorial for a visual guide.

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Mastering the Quadratic Formula: Solve Equations with Ease

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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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