The Solution:
Given:
We are asked to find the vertex of the given equation.
The Vertex formula for a Quadratic Equation is:
From the given equation, we have:
[tex]y=7(x^2-8x+16)+14[/tex][tex]\begin{gathered} y=7x^2-56x+112+14 \\ \\ y=7x^2-56x+126 \end{gathered}[/tex]
In this case,
[tex]\begin{gathered} a=7 \\ b=-56 \\ c=126 \end{gathered}[/tex]
So, the vertex is:
[tex](h,k)=(\frac{-b}{2a},\frac{-(b^2-4ac)}{4a})=(\frac{-(-56)}{2(7)},\frac{-[(-56)^2-4(7)(126)}{4(7)})=(4,-14)[/tex]
Therefore, the correct answer is:
[tex](h,k)=(4,-14)[/tex]
