Answer:
Option B is the correct option.
Step-by-step explanation:
We know that the vertex form of a quadratic's equation is generally expressed as
y = a(x - h)² + k
where (h, k) is called the vertex of the quadratic function
In our case, given the function
[tex]f\left(x\right)=-\frac{1}{2}\left(x+3\right)^2+\frac{25}{2}[/tex]
now comparing the equation with y = a(x - h)² + k
Here:
h = -3
k = 25/2
Therefore, the vertex of the function [tex]f\left(x\right)=-\frac{1}{2}\left(x+3\right)^2+\frac{25}{2}[/tex] is:
(h, k) = (-3, 25/2)
Thus,
The [tex]f\left(x\right)=-\frac{1}{2}\left(x+3\right)^2+\frac{25}{2}[/tex] form most quickly reveals the vertex.
Hence, option B is the correct option.
