Question 1042942
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1. It has the minimum.
   Since it is a parabola opened up.

   It is the parabola opened up, because its leading coefficient is positive.


2.  The minimum is at x = 1.   (Option b)

    Because for the general quadratic function y = ax^2 + bx + c the min/max is at x = {{{-b/2a}}}.  

    It is {{{-(-2)/(2*1)}}} = 1 in your case.


3.  To get the value of the minimum, substitute this x=1 into the formula for your quadratic function. You will get

    f(x) = {{{1^2 - 2*1 - 5}}} = 1 - 2 - 5 = -6.
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See the lesson <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Who-is-who-in-quadratic-equations.lesson>Who is who in quadratic equations</A> in this site.