Completing the Square & Quadratic Formula


Related Topics:
Algebra Word Problems
Common Core (Algebra)
Common Core for Mathematics




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Example, solutions, videos, and lessons to help High School students learn how to use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2* = q* that has the same solutions. Derive the quadratic formula from this form.

Suggested Learning Targets

  • Transform a quadratic equation written in standard form to an equation in vertex form (x - p)2 = q by completing the square.
  • Derive the quadratic formula by completing the square on the standard form of a quadratic equation.
  • Complete the square.
  • Solve quadratic equations, including complex solutions, using completing the square, quadratic formula, factoring, and by taking the square root.
  • Derive the quadratic formula from completing the square. 
  • Recognize when one method is more efficient than the other.
  • Interpret the discriminant.
  • Understand the zero product property and use it to solve a factorable quadratic equation.

Common Core: HSA-REI.B.4a

Completing the Square 1
Part 1 of Showing how to the complete the square to solve quadratic equations.




Completing the Square 2
Part 2 of Showing how to the complete the square to solve quadratic equations.

Completing the Square 3
Part 3 of Showing how to the complete the square to solve quadratic equations.

Completing the Square 4
Part 4 of Showing how to the complete the square to solve quadratic equations.

Completing the Square 5
Part 5 of Showing how to the complete the square to solve quadratic equations.

Quadratic Formula

Deriving the Quadratic Formula
This video shows the proof of the quadratic formula by solving ax2+bx+c by completing the square.

Completing the Square & Quadratic Formula 1
Part 1 of completing the square. This video shows how to derive the quadratic formula by completing the square, and has a song to remember the quadratic formula.

Completing the Square & Quadratic Formula 2
One more example of completing the square to solve a quadratic equation, when the coefficient of x-squared is not 1. The problem is also solved using the quadratic formula.



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