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Quadratic Function: Quadratic Formula | Axis of Symmetry

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The Quadratic Formula:     Previously,   we have proven the Quadratic Formula which is used to find the roots of a particular quadratic function. As we know, the graphical representation of a quadratic function is having a symmetrical shape. Having said that, there will be a line(axis) of symmetry in the graph of any quadratic function.      Base on the Quadratic Formula, every quadratic function will have two roots in general. These roots are      Since the graph of any quadratic function is having a symmetrical shape, hence the axis of symmetry must be equidistance from both its roots. In another words, the axis of symmetry is located at the midpoint of horizontal line connecting both the roots. Hence, the equation for the axis of symmetry can be determined by finding the midpoint between x ₁  and x ₂ .     By doing so, we have successfully derived the equation for the axis of symmetry for a quadratic function based on the Quadratic Formula. What other information that we can obtain
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Quadratic Function: Quadratic Formula | Prove

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     As we have discussed earlier, a general quadratic function  will have the form of  f(x) = ax ² + bx + c ,    where a, b and c are constants and a  ≠  0. Now, I would like to the quadratic formula to you. What exactly is a quadratic formula? A quadratic formula is used to solve a given quadratic function. When we talk about solving a quadratic function, it simply means finding the roots of the quadratic function. Some of you might be curious what is a root? The root that the plant has in their system? No!! The roots of a quadratic function refer the the positions (values of x) on the x-axis at which the quadratic function intersect with the x-axis in a Cartesian Plane. The quadratic formula is given as      Today, we will going to prove the quadratic formula shown above by using the method of Completing The Square . We will start from the general quadratic function. (Proven)           Hence, we have proven the Quadratic Formula which is used to find the roots of a particular quadra
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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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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 | 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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