Completing the Square (Quadratics) [IB Math AA SL/HL]

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This video covers Completing the Square for Quadratics functions and equations. Part of the IB Mathematics Analysis & Approaches SL & HL courses in Topic 2, Functions.

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[edwardchilikawei]

The +4 comes from expanding the brackets it seems:
1: So you get 2(x^2 +4x)+7 from halfing the middle term
2: Now if you look carefully, for "2(x^2 +4x)" we can follow the same rule as we did with the first expression, so we factorize further
2a: 2((x+2)^2)+7
2b: Now focus on the ((x+2)^2) part and expand the brackets. If we expand the brackets, (x+2)(x+2)= x^2 +4x+4. So if you're confused as to where the 4 came from, here it is, it's is there after you expand the brackets after step 2, and 2a.
3.Now 2(x^2 +4x+4)+7 (Remember that the new expression in the brackets resulted from step 2b. So if you multiply 2 with everything in the bracket you get, 2x^2 +8x+8+7
4. Something isn't right... The '+8' is not part of the original expression, so to get balance the equation, -8 to get rid of it. But before you do that, do step 1 again with "2x^2 +8x+8+7", but focus on the 2x^2+8x part
4a. You should half the 8x and thus get-> 2(x+4)^2+7
4b. don't forget that you have to get rid of that 8, so -8 in the end
5. 2(x+4)^2+7+(-8)
6. You then get: 2(x+4)^2 -1
7. Vertex=(-4, -1)

[jonathanboediman]

Thank you very much, your man Travis Robbie introduce you to me and its been very helpful.

[eipimath]

Thanks for sharing! I posted a video on completing the square using remainder theorem. Hope to get your opinion on it.