>>...describe the shape and position of the graph of

              y = (x - h)^2 + g. 

Usually books use the letter "k" where you have "g".  Also they 

usually have the coefficient "a" in front of the first term

              y = a(x - h)² + k

represents the graph of a parabola, a U-shaped graph that has 

vertex at (h,k) and passes through the two points (h±1, k+a).

If "a" is a positive number the parabola opens upward with the 

vertex at the bottom.  If "a" is negative the parabola opens 

downward with the vertex at the top.

Yours is the special case where a=1 and k=g

              y = (x - h)² + g

which represents the graph of a parabola, a U-shaped graph that

opens upward, has vertex at (h,g) and passes through the two

points (h±1, g+1).



Edwin 

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