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Completing the Square

Completing the Square. Learning Targets. Learn how to complete the square This allows us to go from Standard Form to Vertex Form Solving for x in vertex form Be able to freely change the form of any quadratic equation Use knowledge of transformations to represent a function.

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Completing the Square

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  1. Completing the Square

  2. Learning Targets • Learn how to complete the square • This allows us to go from Standard Form to Vertex Form • Solving for x in vertex form • Be able to freely change the form of any quadratic equation • Use knowledge of transformations to represent a function

  3. How to Complete the Square • In order to have a perfect square we need our polynomials or factors to be exactly the same “length” and then multiply them together • Example of a perfect square is • Example of a non perfect square is

  4. How to Complete the Square Most of the quadratics we work with are not perfect squares, so how do you find one?

  5. How to Complete the Square Original Equation: Step 1: Subtract the “lonely” units

  6. How to Complete the Square Original Equation: Step 2: Halve the remaining x’s

  7. How to Complete the Square Original Equation: Step 3: Take those halves and rearrange them • Notice how we have • not lost any of our • original equation 1.5 x’s

  8. How to Complete the Square Original Equation: Step 4:Find out what new value was created and add it to both sides of the equation since we do not want to change anything • Notice how we have • still not lost any of our • original equation

  9. How to Complete the Square Original Equation: Step 5: Now figure out what base’s give us this new figure and write it as factored form

  10. How to Complete the Square Original Equation: Step 6: Don’t forget about the “lonely” units!!!

  11. How to Complete the Square Does this form look familiar?!?! We now have our original equation that was in Standard Form written in Vertex Form!!! But… We should check our work :) IT WORKED!!!

  12. Summary of Steps • Step 1: Subtract the “lonely” units • Step 2: Halve the remaining x’s • Step 3: Take those halves and rearrange them • Step 4:Find out what new value was created and add it to both sides of the equation, since we do not want to change anything • Step 5: Now figure out what base’s give us this new figure and write it as factored form • Step 6: Don’t forget about the “lonely” units!!!

  13. Complete The Square Activity • In our table groups we will work on completing the square using algebra tiles • The goal is for you to see what this method does and why it works • Look for connections between the equation and the manipulative’s

  14. Summary of Steps • Step 1: Subtract the “lonely” units • Step 2: Halve the remaining x’s • Step 3: Take those halves and rearrange them • Step 4:Find out what new value was created and add it to both sides of the equation, since we do not want to change anything • Step 5: Now figure out what base’s give us this new figure and write it as factored form • Step 6: Don’t forget about the “lonely” units!!!

  15. Vertex Form -> Factored Form The last manipulation of forms is going from vertex form to factored form This requires us to solve for x once we are in vertex form Ex:

  16. Example cont. Just like in our standard form we want to set the equation equal to zero in order to find our roots. =0

  17. Example cont. Now we need to solve for x: =25 Don’t forget to graph this and check your answers!

  18. Quick Check

  19. Overall Review Vertex Form Standard Form Expand Complete The Square Distribute Quadratic Eq. or Factor Solve for x Root Midpoint Factored Form

  20. Homework • Worksheet #3

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