To determine the vertex of the function [tex]\( f(x) = -1(x-2)^2 - 3 \)[/tex], we can follow these steps:
1. Identify the form of the equation:
The function is given in the standard vertex form of a quadratic function [tex]\( y = a(x-h)^2 + k \)[/tex].
2. Identify the values of [tex]\( h \)[/tex] and [tex]\( k \)[/tex]:
- In [tex]\( y = -1(x-2)^2 - 3 \)[/tex], the value of [tex]\( h \)[/tex] is 2 and the value of [tex]\( k \)[/tex] is -3.
3. Determine the vertex:
The vertex of the quadratic function [tex]\( y = a(x-h)^2 + k \)[/tex] is given by the point [tex]\( (h, k) \)[/tex].
Therefore, for the function [tex]\( f(x) = -1(x-2)^2 - 3 \)[/tex]:
- [tex]\( h = 2 \)[/tex]
- [tex]\( k = -3 \)[/tex]
So, the vertex of the function is the point [tex]\( (2, -3) \)[/tex].
Hence, the correct answer is:
[tex]\[ (2, -3) \][/tex]
