The equation they're talking about is f(x) = a(x - h)² + k, by the way.
A parabola is ... a quadratic equation. The vertex is the max ...
The value of h moves. .. horizontally ... the value of k moves ... vertically.
The value of a determines ... upward ... If a is greater than zero, ... upward. If a is less than zero, ... downward.
|a|>1 is narrow, |a|<1 is wide