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Which point represents the vertex of the graph of the function [tex]$f(x)=-1(x-2)^2-3$[/tex]?

A. [tex](-2, -3)[/tex]
B. [tex](2, -3)[/tex]
C. [tex](3, -2)[/tex]
D. [tex](3, 2)[/tex]
E. [tex](2, 3)[/tex]

Sagot :

GinnyAnsweridn
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]
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