About Myself

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    Hello, everyone. I am a crazy mathematics lover who enjoy proving some mathematical formulae. Besides, I am also interested in helping people in understanding some fundamental mathematical concepts. I wish I am able to share some of my knowledge here with you. I hope that everyone who had visited this blog are able to establish a better understanding in the field of mathematics. 

    Once again, thank you for visiting my blog. I wish you all the best in your future undertakings! Before that, do not forget to LIKE, SHARE and SUBSCRIBE to my blog and my YouTube channel as well. See you!!

    If you have any enquiries, kindly e-mail me at 99madmath@gmail.com. Besides, you can also reach to me via Facebook.

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Quadratic Function: Completing The Square | Prove

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     In general, a quadratic function will have the form of  f(x) = ax ² + bx + c ,    where a, b and c are constants and a  ≠ 0.    Do remember that in order to perform the method of completing the square, the coefficient of the  x ²  term in the quadratic expression  MUST  be equal to 1.      In this case, we are going to prove  where k is also a non-zero arbitrary constant.     To prove and thoroughly understand how the method of completing the square works on a quadratic function, we can actually visualize it by using paper-folding technic. In order to do so, the materials that are required include an A4 sized paper, a pen, a cellophane tape and a pair of scissors or a paper cutting blade.      The procedures needed are as shown as follow. All the figures shown in the procedures are the top view of the A4 sized paper.     1.  Fold the A4 sized paper as shown in the figure below according to the sequence indicated.    2. Unfold the A4 sized paper and l abel the length of each side o
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Quadratic Function: Completing The Square | Derivation

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    In the previous post , we have proven the equation that is responsible for the method of completing the square in a quadratic function. The equation that we have proven previously is  ----------------------------------------------- (1)                         where k is a non-zero arbitrary constant.     Now, what will happen to equation (1) if the constant, k has a positive value? What if the constant, k has a negative value? Let us try to find it out.     (A) Positive Value of the Constant, k           (B) Negative Value of the Constant, k     Hence, we have derived the two equations which is normally used for the method of completing the square in an quadratic function.   Lastly, I hope that you enjoyed reading the post and learning from it. Please do not forget to  LIKE ,  SHARE  and  SUBSCRIBE  to my  blog  and my  YouTube channel  as well. Thank you and have a nice day!
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Quadratic Function: Completing The Square | Verification

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    In the  previous post , we have derived  two equations which is normally used for the method of completing the square in an quadratic function. The above-mentioned equations are shown below, where the constant, m has a positive value.     Today, we will verify the two equations above to ensure that the two equations are valid. To verify these equations, what we have to do is to expand and simplify the right hand side (RHS) of the equations and compare it with the left hand side (LHS) of the equations. As long as RHS = LHS, the equation will be true.     Equation (1)     Equation (2)        As we can see, the two equations which is normally used for the method of completing the square in an quadratic function have been verified.   I hope that you enjoyed reading the post and learning from it. Please do not forget to  LIKE ,  SHARE  and  SUBSCRIBE  to my  blog  and my  YouTube channel  as well. Thank you and see you in the next blog post!
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