Answer:
The correct option is;
The variable x has a coefficient
Explanation:
The given vertex form of a quadratic function and the quadratic function can be written as follows;
Vertex form of a quadratic function, f(x) = (3·x + 1/3)² + 8/9
The quadratic function, f(x) = 9·x² + 2·x + 1
The vertex form of a quadratic function f(x) = a·x² + b·x + c is f(x) = a·(x - h)² + k
Where;
h = -b/(2·a) = -2/(2×9) = -1/9
k = f(h) = f(-1/9) = 9 × (-1/9)² + 2 × (-1/9) + 1 = 8/9
Which gives the vertex form a s f(x) = 9·(x - (-1/9))² + 8/9
f(x) = 9·(x + 1/9)² + 8/9
Therefore, f(x) = (3·x + 1/3)² + 8/9 is not the vertex form of f(x) = 9·x² + 2·x + 1 because the variable x has a coefficient.