Problem 61145. Translating even-degree polynomial by its vertex to the origin

Luisa

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Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.
Find 
d (d>0) the shifting distance of the above translation;
v the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;
h the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.
Hint. Compare to the Problem 61143.
input: p
output: [d, v, h]