![]() This is actually the vertex form of the original equation, y = x 2 + 8x – 2 and the vertex is (-4, -18). Let us factor the perfect square and combine the extra values which would lead to: Thus, we get a perfect square, x 2 + 8x + 16, with some extra values. So the equation looks like, y = x 2 + 8x + 16 – 2 – 16. Let us add and subtract 16 within one part of the equation. So, what would be the value of c to make this a perfect square?Ĭ should have to be 16 to make the equation a perfect square. But within this equation it is not the same. As we have said before, to be a perfect square you should square the half of b to get c. This equation cannot be factorized and apparently it is not a perfect square either. Let us take another example of an equation for instance. Here we are adding and subtracting 3 within one part of the equation without changing the value of the equation. Similarly, we can add and subtract the same values from one part of the equation simultaneously. However, it is not an appropriate purpose to add in this equation, but mathematically, it does not change the value of the equation. ![]() For instance, we can add 3 to each part of the equation. We can add or subtract values in the equation without changing the original value of the equation. Let us take an example of an equation, y=5x – 9. So, from the above example we can say that half of b is equal to –(16/2) = -8. Thus we can say that squaring half of b is always equivalent to c. Theory #2: Finding the pattern within squaresįrom the above quadratic equation, we can say that it has a pattern since the leading co-efficient is a perfect square. X 2 – 16x + 64 is a square which can again be denoted as (x – 8) 2. Theory #1: Squares can be easily factorizedĪny quadratic equation that is a square can be easily factored. We have a few theories regarding this which is listed below. The main goal of CTS or Completing the Square is to take any quadratic equation that is not a perfect square and change it into a squared one without even changing the value. Let us start with some examples over the application of the technique called “Completing the Square”. Using this technique, we can change a quadratic equation into a perfect square and you would get to know that it can be easily factorized. Let us start with a technique called “Completing the Square”. In this article, we would show you all the ideal concepts regarding vertex form and vertex formula. You can certainly do so if you understand what a perfect square is. To change a quadratic equation from a standardized form to a vertex form is quite easy to derive.
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