f(x) = a(x - h)^2 + k is the standard form of a quadratic function.
(h, k) gives us the coordinates of the vertex.
The original or base function f(x) = x^2 has its vertex at (0, 0). This means that (h, k) translates or moves that vertex. The translation is h units to the left, and k units upward if h and k are positive. The translation is h units to the right and k units downward if h and k are negative.
Remember that h is subtracted from x in the standard form. So in g(x) = (x - 8)^2, the graph of f(x) = x^2 is translated 8 units to the left.
Finally, a gives us the vertical stretch. It multiplies (x - h) so that the graph is elongated or "flattened".
If a > 1 or a < -1, then f(x) = x^2 is elongated; if it is -1< x < 1 (except a = 0), then it is flattened.
If a is negative, then the graph is also turned upside down. It opens downwards.