[tex]y(x) = x^{2} + 14x + 48[/tex]
[tex]y = x^{2} + 14x + 49 - 49 + 48 \text{ *}[/tex]
[tex]y = (x + 7)^{2} - 1[/tex]
[tex]\boxed{y + 1 = (x + 7)^{2}}[/tex]
* Completing the square:
The whole premise behind 'completing the square' was to isolate the x variable by itself in the form of a quadratic function. To understand this concept, we need to look back at the whole idea that when expanding a binomial with degree 2, we will get a predictable pattern specifically:
[tex](x + y)^{2} = x^2+\boxed{2}xy+y^2[/tex]
This allowed us to then create a new concept (completing the square), where we attempt to revert back to our simplest form. To understand more about the history and proof, you can search up: "Completing the square".
