DACC Spring 2025 CCDM 114 - Quadratic Formula Concepts

Key Concepts of Quadratic Equations

  • Quadratic Formula: The general form of the quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0. The solutions can be found using the quadratic formula:
    x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

  • Solving Quadratic Equations: Use the quadratic formula to get the values of xx for the following equations, substituting the values of aa, bb, and cc accordingly.

Examples to Solve

  1. Example (a): 6x2−3x−4=06x^2 - 3x - 4 = 0

    • Here, a=6a = 6, b=−3b = -3, c=−4c = -4
    • Substituting into the quadratic formula will yield the solutions for xx.

  2. Example (b): 4x2−4x−1=04x^2 - 4x - 1 = 0

    • Here, a=4a = 4, b=−4b = -4, c=−1c = -1
    • Apply the quadratic formula to find xx.

  3. Example (c): 2x2+9x−5=02x^2 + 9x - 5 = 0

    • Here, a=2a = 2, b=9b = 9, c=−5c = -5
    • Use the formula to solve for xx.

  4. Example (d): 3x2−5y+2=03x^2 - 5y + 2 = 0

    • Identify coefficients for the equation and utilize the quadratic formula.

Key Points for the Exam

  • The quadratic formula will be provided on the exam.
  • Remember to rearrange the equation to standard quadratic form if required.
  • Pay attention to signs and coefficients when substituting into the formula.