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Examples of Quadratic Equation

Examples of Quadratic Equation

quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable. One absolute rule is that the first constant “a” cannot be a zero.

Standard Form Equations

Here are examples of quadratic equations in the standard form (ax² + bx + c = 0):

  • 6x² + 11x – 35 = 0
  • 2x² – 4x – 2 = 0
  • -4x² – 7x +12 = 0
  • 20x² –15x – 10 = 0
  • x² –x – 3 = 0
  • 5x² – 2x – 9 = 0
  • 3x² + 4x + 2 = 0
  • -x² +6x + 18 = 0

Here are examples of quadratic equations lacking the linear coefficient or the “bx”:

  • 2x² – 64 = 0
  • x² – 16 = 0
  • 9x² + 49 = 0
  • -2x² – 4 = 0
  • 4x² + 81 = 0
  • -x² – 9 = 0
  • 3x² – 36 = 0
  • 6x² + 144 = 0

Here are examples of quadratic equations lacking the constant term or “c”:

  • x² – 7x = 0
  • 2x² + 8x = 0
  • -x² – 9x = 0
  • x² + 2x = 0
  • -6x² – 3x = 0
  • -5x² + x = 0
  • -12x² + 13x = 0
  • 11x² – 27x = 0

Here are examples of quadratic equation in factored form:

  • (x + 2)(x – 3) = 0 [upon computing becomes x² -1x – 6 = 0]
  • (x + 1)(x + 6) = 0 [upon computing becomes x² + 7x + 6 = 0]
  • (x – 6)(x + 1) = 0 [upon computing becomes x² – 5x – 6 = 0
  • –3(x – 4)(2x + 3) = 0 [upon computing becomes -6x² + 15x + 36 = 0]
  • (x − 5)(x + 3) = 0 [upon computing becomes x² − 2x − 15 = 0]
  • (x – 5)(x + 2) = 0 [upon computing becomes x² – 3x – 10 = 0]
  • (x – 4)(x + 2) = 0 [upon computing becomes x² – 2x – 8 = 0]
  • (2x+3)(3x – 2) = 0 [upon computing becomes 6x² + 5x – 6]

Here are examples of other forms of quadratic equations:

  • x(x – 2) = 4 [upon multiplying and moving the 4 becomes x² – 2x – 4 = 0]
  • x(2x + 3) = 12 [upon multiplying and moving the 12 becomes 2x² – 3x – 12 = 0]
  • 3x(x + 8) = -2 [upon multiplying and moving the -2 becomes 3x² + 24x + 2 = 0]
  • 5x² = 9 – x [moving the 9 and -x to the other side becomes 5x² + x – 9]
  • -6x² = -2 + x [moving the -2 and x to the other side becomes -6x² – x + 2]
  • x² = 27x -14 [moving the -14 and 27x to the other side becomes x² – 27x + 14]
  • x² + 2x = 1 [moving “1” to the other side becomes x² + 2x – 1 = 0]
  • 4x² – 7x = 15 [moving 15 to the other side becomes 4x² + 7x – 15 = 0]
  • -8x² + 3x = -100 [moving -100 to the other side becomes -8x² + 3x + 100 = 0]
  • 25x + 6 = 99 x² [moving 99 x2 to the other side becomes -99 x² + 25x + 6 = 0]

There are many different types of quadratic equations, as these examples show.


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