Question 116801
Given:
.
{{{f(x)= x^2+6x-2}}}
.
This function is of the standard form:
.
{{{y = ax^2 + bx + c}}}
.
Recall the quadratic formula that says for a function of this form the solutions for x are:
.
{{{x = -b/(2*a) +- sqrt( b^2-4*a*c )/(2*a) }}}
.
The first term on the right side (that is {{{-b/(2*a)}}} will give you the value for x
at the vertex of the parabolic graph for {{{y = ax^2 + bx + c}}}
.
Comparing the given function with the standard form you can see that a in the standard form
[the multiplier of the {{{x^2}}}] is +1 in the given problem, and b in the standard form
[the multiplier of the {{{x}}}] is +6 in the given problem, and c (which we don't need) in 
the standard function is -2 in the given problem.
.
All you now have to do to solve this problem is plug the values for a and b into {{{-b/(2*a)}}}
and you get that the value of x at the vertex is:
.
{{{-b/(2*a) = -(+6)/(2*1) = -6/2 = -3}}}
.
So the answer to your problem is h = -3
.
Here's the graph of the equation {{{y = x^2 + 6x -2}}} (shown in red) to help you validate 
the answer. The green line is a vertical line through the vertex. It shows you that the
vertex has -3 as the value for its x:
.
{{{graph(400,400,-10,5,-15,5,x^2 +6x -2,3000(x+3)/3)}}}
.
Hope this helps you to understand the problem a little better.
.