Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k, that vertically transforms the polynomial p by scaling (1) the entire function and (2) only the leading coefficient (see figure below). To compare both cases, (1) and (2), find
  • V0, the m0×2 matrix that represents the vertex of the original polynomial p;
  • V1, the m1×2 matrix that represents the scaled vertex for case 1:
  • V2, the m2×2 matrix that represents the scaled vertex for case 2;
where 1 <= m0, m1, m2 < n and n stands for the degree of polynomial (see Hint). Return the first column of each matrix sorted by increasing x-values (in ascending order), while the y-value of the vertex in the second column.
Hint. The vertex of an even-degree polynomial is not necessarily unique, i.e., the global extremum may be reached at m, multiple distinct, x-values.
input: (p, k)
output: [V0, V1, V2]
Comparing scales
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David Hill Matthew Bolyard

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