Practicing the Quadratic Formula

Jul 15, 2024

Practicing the Quadratic Formula

Introduction

  • Instructor: John from TC Math Academy
  • Objective: Practice solving quadratic equations using the quadratic formula
  • Quadratic Formula: A formula to solve quadratic equations
  • Alternative methods: If possible, solve using other techniques before using the quadratic formula

Steps to Approach Quadratic Equations

  1. Identify Quadratic Equation: Recognize it's a second-degree polynomial equation (highest power is 2)
  2. Two Solutions: As per the Fundamental Theorem of Algebra
  3. Determine Solution Types: Real or Complex/Imaginary numbers

Methods to Solve Quadratic Equations

  1. Square Root Method: Applicable if the equation is in the form x² = a number
  2. Factoring: If the trinomial can be factored
  3. Quadratic Formula:
    • Use if other methods don't apply
    • Memorize: quadratic formula
    • Apply: Standard form ax² + bx + c
    • Formula: x = (-B ± √(B² - 4AC)) / 2A
  4. Completing the Square: Another useful technique

Example Problem

Given Equation

  • x² - 4x = 8

Solution Steps

  1. Move 8 to left side: x² - 4x - 8 = 0
  2. Identify coefficients: a = 1, b = -4, c = -8
  3. Plug into quadratic formula: 4. x = (-(-4) ± √((-4)² - 4(1)(-8))) / 2(1) 5. Simplify under √:
    • 16 + 32 = 48
    1. Simplify radical √48:
      • 48 = 16*3 → √48 = 4√3
    2. Substitute back and simplify:
      • x = (4 ± 4√3) / 2
      • Factor out 4 and simplify: 2 ± 2√3
    3. Final solution:
      • x = 2 + 2√3
      • x = 2 - 2√3

Additional Tips

  • Always check if the radical part can be simplified
  • Use parentheses when substituting values to avoid mistakes

Conclusion

  • Practice quadratic formula to mastery

  • Resolve any gaps in understanding related concepts (factoring, square roots)

  • Continuous practice essential for algebra success

  • Check out more resources and videos on TC Math Academy for comprehensive algebra help

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Closing

  • Wishing you the best in your mathematical journey!