Answer:
B
Step-by-step explanation:
There are several ways to find the vertex of function such as formula, completing the square or differential.
I will use the formula to find the vertex.
We are given the function:
[tex] \displaystyle \large{f(x) = - {x}^{2} + 4x - 3}[/tex]
Vertex Formula
Let (h,k) = vertex
[tex] \displaystyle \large{ \begin{cases} h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a} \end{cases}}[/tex]
From the function, compare the coefficients:
[tex] \displaystyle \large{a {x}^{2} + bx + c = - {x}^{2} + 4x - 3}[/tex]
Therefore:-
[tex] \displaystyle \large{ \begin{cases} h = - \frac{4}{2( - 1)} \\ k = \frac{4( - 1)( - 3)- {4}^{2} }{4( - 1)} \end{cases}}[/tex]
Then evaluate for h-value and k-value.
[tex] \displaystyle \large{ \begin{cases} h = - \frac{4}{ - 2} \\ k = \frac{4( 3)- 16}{ - 4} \end{cases}} \\ \displaystyle \large{ \begin{cases} h = 2 \\ k = \frac{12 - 16}{ - 4} \end{cases}} \\ \displaystyle \large{ \begin{cases} h = 2 \\ k = \frac{ - 4}{ - 4} \end{cases}} \\ \displaystyle \large{ \begin{cases} h = 2\\ k = 1\end{cases}}[/tex]
Therefore the vertex is (h,k) = (2,1)
