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The Quadratic Formula

What is the Quadratic Formula?

question
Answer:
The quadratic formula is : Picture of the quadratic formula


What does this formula tell us?

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Answer:
The quadratic formula will calculate the solutions of any quadratic equation.


What is a quadratic equation?

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Answer:
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


Ok, but what is a 'solution'?

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Answer:
Well a solution can be thought in two ways:
Algebra: For any quadratic equation of the form f(x) = ax2+bx+c, the solution is when f(x) = 0.
Geometry The solution is where the graph of a quadratic equation (a parabola) is intersects the x-axis.
solutions
This, of course, only applies to real solutions.
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)

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
Quadratic Formula Song
A catchy way to remember the quadratic formuls is this song (pop goes the weasal)
Practice Problems


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)
In this quadratic equation,
y = x² − 4x + 5 and its solution
  • a =1
  • b = −4
  • c = 5
Below is a picture of this quadratic's graph