### COMPLETING THE SQUARE

Completing the square method is used to convert the quadratic equation from general form ax^2+bx+c to vertex form a(x-h)^2 +k.

Application of completing the square method

1. Solving quadratic equation

2. Converting to vertex form

3. Graphing a quadratic function

#### Completing The Square Method Steps

- Start with the quadratic equation
- Divide through by the coefficient of x^2
- Take half of the coefficient of x and square it.
- Add and subtract the squared term inside the parentheses.
- Factor the perfect square trinomial and simplify
- Combine like terms
- Simplify further if possible

#### Application Of Completing The Square Methods

Completing the square method has various real world an mathematical application.

1. Solving quadratic equations

The main application of this method is to solve quadratic equation. Completing square method is a quadratic equation solver. If you want to solve the quadratic equation first you need to change the standard form of quadratic equation into a perfect square trinomial. After that by taking the square roots on both sides we can find the solution.

2. Graphing a quadratic equation

Using the complete square method we can change the standard form into a vertex form. Graphing a quadratic function is much simpler in the vertex form than in the standard form. a(x-h)^2 +k where (h,k) is the vertex of parabola.

3.Optimization Problems

Maximum or Minimum values can be found using the completing square methods. To find the maximum and minimum standard form quadratic equation should be converted to vertex form. a(x-h)^2 +k where (h,k) is the vertex of parabola.

4. Physics Equations

Completing the square method has various application in physics. Some kinematics or laws of motion equations can be in a quadratic equation. By changing to vertex form we can find the solutions