Answer
The required value is\[\left( -1,\ 5 \right)\]
Work Step by Step
The quadratic function in its standard form can be written as
$f\left( x \right)=a{{\left( x-h \right)}^{2}}+k,\,\,\,\,\,\,\,\,a\ne 0$.
Here, $a,\ h,\ k$ are constants and $x$ is a variable. The graph of $f\left( x \right)$ is a parabola which is symmetric about the line $x=h$.
Now, the coordinates of the vertex of the parabola are $\left( h,\ k \right)$.
Let us consider the given function $f\left( x \right)=-2{{\left( x+1 \right)}^{2}}+5$.
Compare the function with the standard form.
Hence, the point $\left( h,\ k \right)$ is $\left( -1,\ 5 \right)$.
