The given function is
[tex]f(x)=x^2-2x-5[/tex]
All quadratic functions represent a parabola. If the quadratic term is positive, the parabola opens up, if the quadratic term is negative, the parabola opens down.
In this case, we observe a positive quadratic term, so the parabola opens up, which means the function has a minimum.
To find the minimum of the function, we need to find its vertex (h,k), where
[tex]h=-\frac{b}{2a}[/tex]
a = 1 and b = -2.
[tex]h=-\frac{-2}{2(1)}=\frac{2}{2}=1[/tex]
Then, evaluate the function to find k.
[tex]f(1)=(1)^2-2(1)-5=1-2-5=1-7=-6[/tex]
The k-coordinate of the vertex refers to the minimum value.
Therefore, the answer is -6.
