We can find the vertex of the function by expanding the function and replacing in the following expression:
[tex]x=-\frac{b}{2a}[/tex]Now, we expand the function:
[tex]y=(x-5)^2+2\Rightarrow y=x^2-10x+27[/tex]Now, we replace in the expression:
[tex]x=-\frac{(-10)}{2(1)}=5[/tex]Now, we proceed as follows:
We plug the value we got [That is the x-component of the vertex] in the equation and solve for x, that is:
[tex]y=(5)^2-10(5)+27\Rightarrow y=2[/tex]So, the vertex is found in the point (5, 2).
