Quadratic Formula

• What is the quadratic formula?

  x = -b ± √(b² - 4ac) / 2a
• In the equation 3xc² + 7x + 2 = 0, what is the value of a?


  3
• In the equation 3xc² + 7x + 2 = 0, what is the value of b?


  7
• In the equation 3xc² + 7x + 2 = 0, what is the value of c?

  2
• How do you find the roots of the equation x² - 5xc + 2 = 0 using the quadratic formula?

  Substitute a, b, c into the formula
• What are the roots of the equation x² - 5xc + 2 = 0?

  x = 5 ± √17 / 2
• What is the value of a in the equation x² + 3x - 3 = 0?

  1
• What is the value of b in the equation x² + 3x - 3 = 0?


  3
• What is the value of c in the equation x² + 3x - 3 = 0?

  -3
• How do you calculate the roots of the equation x² + 3x - 3 = 0?

  Use the quadratic formula with a, b, c
• What are the roots of the equation x² + 3x - 3 = 0?

  x = 3 ± √21 / 2
• What is the value of a in the equation 2x² - 4x - 1 = 0?


  2
• What is the value of b in the equation 2x² - 4x - 1 = 0?

  -4
• What is the value of c in the equation 2x² - 4x - 1 = 0?

  -1
• How do you find the roots of the equation 2x² - 4x - 1 = 0?

  Apply the quadratic formula with a, b, c
• What are the roots of the equation 2x² - 4x - 1 = 0?

  x = 4 ± √8 / 4
• What is the value of a in the equation 1 - x² - 8ox = 0?


  1
• What is the value of b in the equation 1 - x² - 8ox = 0?


  8
• What is the value of c in the equation 1 - x² - 8ox = 0?

  0
• How do you calculate the roots of the equation 1 - x² - 8ox = 0?

  Use the quadratic formula with a, b, c
• What is the significance of the discriminant in the quadratic formula?

  It determines the nature of the roots
• What are the steps to solve a quadratic equation using the quadratic formula?

  1. Identify coefficients a, b, c
  2. Substitute into the formula: x = -b ± √(b² - 4ac) / 2a
  3. Simplify to find the roots
• What does the discriminant (b² - 4ac) indicate in a quadratic equation?

  • Positive: Two distinct real roots
  • Zero: One real root (double root)
  • Negative: No real roots (complex roots)
• How do the roots of a quadratic equation relate to its graph?

  • Roots are x-intercepts of the graph
  • Indicates where the parabola crosses the x-axis