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Completing the Square: Solving Quadratic Equations

Learn how to complete the square to solve quadratic equations, including special cases and complex solutions. Find the vertex form, factor perfect square trinomials, and simplify expressions.

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Completing the Square: Solving Quadratic Equations

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  1. 2.1.8 Completing the Square Essential Questions: How do you complete the square and use it for solving?

  2. Solving with special cases

  3. Main Idea & Vocabulary • Today, we are going to learn another way to solve for the zeros of a quadratic equation. • Today, the c value is missing. • When completing the square, you add a term to the expression x2 + bx so you make a perfect square trinomial. • Formula to complete the square:

  4. Completing the Square

  5. Ex 1-Completing the Square

  6. Solve by Completing the Square Step 1: Use form x2 + bx = c (never have an a) Step 2: Find (b/2)2 Step 3: Complete the square by adding it to the equation Step 4: Factor the trinomial Step 5: Solve the equations

  7. Completing the square

  8. Complex Solutions

  9. Completing the square

  10. Completing the Square

  11. Completing the square

  12. Vertex Form • Complete the square for vertex form • Factor out a, if a is not 1 • Complete the square • Balance the equation by doing the opposite amount on the same side • Factor the perfect square trinomial • Simplify

  13. Completing the square

  14. Application

  15. Application

  16. Summary • Answer the essential question in detailed, complete sentences. How do you complete the square and use it for solving? • Write 3-5 study questions in the left column to correspond with the notes.

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