Solving Problems including Quadratic Equations

• Quadratic equation


  An equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0
• Solving quadratic equations


  1. Understand the problem

  2. Write the equation

  3. Solve the equation by factoring or using the quadratic formula
• Rectangular table


  • Area = 27 square feet
  • Perimeter = 24 feet
• Solving for dimensions of rectangular table

  1. Write the equation: x^2 + (-12)x + 27 = 0

  2. Solve by factoring: x = 3 or x = 9

  3. Length = 9 feet, Width = 3 feet
• Sum of two numbers


  The sum of the two numbers is 19
• Sum of squares of two numbers

  The sum of the squares of the two numbers is 193
• Solving for the two numbers

  1. Let x be one number, 19-x be the other

  2. Write the equation: x^2 + (19-x)^2 = 193

  3. Solve by factoring: x = 7, 19-x = 12
• Inclined ramp


  • Rise = x meters
  • Run = x + 7 meters
  • Length = x + 8 meters
• Solving for the sides of the ramp

  1. Write the equation using Pythagorean Theorem: (x+8)^2 = x^2 + (x+7)^2

  2. Solve by factoring: x = 5, Rise = 5 meters, Run = 12 meters, Length = 13 meters