Suppose an object moves along the y axis so that its location is y​f(x)=x^2 +x at time x​ (y is in​ meters, x is in​ seconds). Find ​(A) The average velocity​ (the average rate of change of y with respect to​ x) for x changing from to 2 to 4.
​(B) The average velocity for x changing from 2to 2+ h.
​(C) The instantaneous velocity at x=2 second.

Okay, so the formula you're looking at is y = a(x - h)2+ k and you're trying to find your vertex, or the turning point, which is (h,k)

With the given  the h is going to be 2 and the k will be 8 giving you the vertex of (2,8) or, in this case, the turning point of this graph.

The way you get a positive 2 for h is because in the formula you have an (x-h) and since the h=-2 anytime you have a number (x) subtracted by a negative number, (--2) the negatives cancel out leaving a positive 2 

So you're answer is (2,8)