Pre Calculus 11 Notes

By: Gen L.

In partnership with Hyperion University, 2023

Lesson 4: Completing the Square

Why Complete the Square?

  • Vertex Form is more useful than standard form.

    • Less information to solve for,
    • Most of the information we need to make a graph.

  • IMPORTANT: It is not a formula, it is a
    process.

Example 1:

  • Convert into vertex form.
  1. Separate all terms.
    • , is the constant we'll need later.
  2. Determine .
  3. Plug in , to get our trinomial

Example 1, cont:

  1. Factor.
  2. Simplify.
  • Final Function:

Example 2:

  • Convert into vertex form.
  1. Seperate all terms.
    • Remove common factor of terms.
  2. Determine .

Example 2, cont:

  1. Plug in .
  2. Factor.
  3. Simplify.
  • Final Function:

Example 3:

  • Convert into vertex form.
    • Why 12? must be multipled by when added to .

Example 4:

  • Convert into vertex form.

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