QUADRATICS COMPLETING THE SQUARE (easy examples) PPT

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QUADRATICS COMPLETING THE SQUARE (easy examples) PPT

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  1. A Mathslay3r

    Slide 1 - A Mathslay3r

    • Production
    • A Mathslay3r
    • Production
    • A Mathslay3r
    • Production
    • A Mathslay3r
    • Production
    • Quadratics
    • Completing the Square
    • Part One
    • Easy Examples
    • @2015
  2. A Mathslay3r

    Slide 2 - A Mathslay3r

    • Production
    • A Mathslay3r
    • Production
    • A Mathslay3r
    • Production
    • @2015
    • This is for every math underdog that never got it..
  3. @2015

    Slide 3 - @2015

    • There are two ways to show Completing the Square:
    • One method uses function notation
    • The other does not.
    • This video will focus on the one that does not
    • because most often it is taught this way.
    • The other way will be shown in a separate video.
  4. Everyone wants to use  the quadratic formula

    Slide 4 - Everyone wants to use the quadratic formula

    • It’s known for being easy.
    • It works on everything.
    • But then comes that fateful day,
    • when you are in your first college math class.
  5. And, you have an epiphany.

    Slide 5 - And, you have an epiphany.

    • Which is sort of like having a cow….
    • But much, much worse
  6. As you scan the prof’s syllabus, your life is….well….you get the picture

    Slide 6 - As you scan the prof’s syllabus, your life is….well….you get the picture

  7. Slide 8

    • @2015
    • No doubt, the quadratic formula is a beautiful thing.
  8. Slide 9

    • @2015
    • But without a calculator,
    • it can be a landmine of potential mistakes.
  9. Slide 10

    • @2015
    • A technique called
    • Completing the square Is more difficult to learn, but easier to remember and with practice requires fewer steps
  10. Before you start…...

    Slide 11 - Before you start…...

    • Know that a quadratic like:
    • Factors to:
    • Which is stated as:
    • Has the square root of:
  11. Before you start…...

    Slide 12 - Before you start…...

    • Know that:
    • Is the standard algebraic form
    • of a quadratic equation.
    • Where are coefficients
  12. Before you start…...

    Slide 13 - Before you start…...

    • Know that: must be equal to one
    • When: You begin Completing the Square.
  13. Solve by Completing the Square

    Slide 14 - Solve by Completing the Square

  14. Okay, so that was a little too fast…but you will pick up speed like that soon…

    Slide 15 - Okay, so that was a little too fast…but you will pick up speed like that soon…

    • Here’s the Slo-mo
    • Subtract ‘c’ from both sides
    • Take ‘b’ split it in half
    • Square that & Add result to both sides
  15. Factor the right side

    Slide 16 - Factor the right side

    • simplify
  16. Root out both sides

    Slide 17 - Root out both sides

    • Plus or minus on the right
  17. Get ‘x’ by itself

    Slide 18 - Get ‘x’ by itself

  18. Solve by Completing the Square

    Slide 19 - Solve by Completing the Square

    • Add 21 to both sides
    • Take ‘b’ split it in half, then square it
    • Add the result to both sides
    • Factor the right, simplify the left
  19. Solve by Completing the Square

    Slide 20 - Solve by Completing the Square

    • Root out both sides
    • Plus or minus on the right
    • Simplify
    • Done!
  20. Solve by Completing the Square

    Slide 21 - Solve by Completing the Square

    • Add 20 to both sides
    • Take ‘b’ split it in half, then square it
    • Add the result to both sides
    • Factor the right, simplify the left
  21. Solve by Completing the Square

    Slide 22 - Solve by Completing the Square

    • Check your work
  22. What if the b-coefficient is odd?

    Slide 23 - What if the b-coefficient is odd?

    • What you add to both sides will be a fraction
    • Other wise the process is the same
  23. What if the b-coefficient is odd?

    Slide 24 - What if the b-coefficient is odd?

    • What you add to both sides will be a fraction
    • Other wise the process is the same
  24. What if the b-coefficient is odd?

    Slide 25 - What if the b-coefficient is odd?

  25. What if the b-coefficient is odd?

    Slide 26 - What if the b-coefficient is odd?

  26. What if the b-coefficient is odd?

    Slide 27 - What if the b-coefficient is odd?