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The Quadratic Formula

Solve quadratic equations

Use The Quadratic Formula Calculator to see Quadratic Formula in Action! Calculator will solve any quadratic equation you type in (even if roots are imaginary)

Solving Quadratic Equations | The Quadratic Formula | factoring quadratic equations|completing the square in math| interactive parabola | Quadratic Formula Calculator | formula for sum and product of roots
The quadratic formula will calculate the solutions of any quadratic equation.
A quadratic equation is an equation that can be written as
    ax ² + bx + c where a ≠ 0
In other words, a quadratic equation must have a squared term as its highest power
    Examples of quadratic equations
  • y = 5x² + 2x + 5
  • y = 11x² + 22
  • y = x² − 4x +5
  • y = −x² + 5
    Examples of equations that are not quadratic
  • y = 11x + 22
  • y = x3 − 4x² +5x +5
  • y = 2x3 − 4x²
  • y = −x4 + 5

The solution of a quadratic equation is the value of x when you set the equation equal to zero
i.e. When you solve the following general equation: 0 = ax² + bx + c
Given a quadratic equation: ax ² + bx + c
    The quadratic formula below will solve the equation for zero
The quadratic formula is : Picture of the quadratic formula
Examples of the quadratic formula to solve an equation
  • Example 1
      Quadratic Equation: y = x² + 2x + 1
    • a = 1
    • b = 2
    • c = 1
      • Using the quadratic formula to solve this equation just substitute a,b, and c into the general formula:
      example of quadratic formula
      Below is a picture representing the graph of
      y = x² + 2x + 1 and its solution
    Picture of graph of solved quadratic formula
Use the quadratic formula to find the solutions to the following equation:
y = x² − 2x + 1 and its solution
Answer
Use the quadratic formula to find the solutions to the following equation:
y = x² − x − 2 and its solution
Solution(s)
Use the quadratic formula to find the solutions to the following equation:
y = x² − 1 and its solution
Answer
Calculate the solutions of the the quadratic equation below by using the quadratic formula :
y = x² + 2x − 3 and its solution
Answer
Use the quadratic formula to find the solutions to the following equation:
y = x² + 4x − 5 and its solution
Solution(s)
Use the quadratic formula to find the solutions to the following equation:
y = x² − 4x + 5 and its solution
Solution(s)
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