DACC Spring 2025 CCDM 114 - Quadratic Formula Concepts

Key Concepts of Quadratic Equations

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

• Solving Quadratic Equations: Use the quadratic formula to get the values of x for the following equations, substituting the values of a, b, and c accordingly.

Examples to Solve

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

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

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

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

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

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

4. Example (d): 3x^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.