Geogebra Function Investigation - Vertex Form
Vertex form
[a] Controls horizontal shrink/stretch and end behavior/concavity of the graph. Larger values of a will shrink the graph horizontally, while smaller ones stretch it. A positive a-value indicates that the graph opens upward with y always approaching positive infinity, while the negative a-value indicates that it opens downward with y always approaching negative infinity.
[h] Controls horizontal shift. A positive value indicates that the vertex is rightward by that amount from the vertex of the parent graph of y=x^2 (0,0), and a negative value indicates that it is shifted leftward by that amount. The value is positive if the sign before it is -, and negative if the sign is +.
[k] Controls vertical shift. A positive value indicates that the vertex is shifted up by that amount from the vertex of the parent graph of y=x^2 (0,0), and a negative value indicates that it is shifted downward by that amount.