Why is f(x)=(3x+13)2+89 not the vertex form of f(x)=9x2+2x+1?

Step-by-step explanation:

Given function in the vertex form is,

f(x) = (3x + 13)² + 89

    = --------(1)

Vertex of the parabola →

If the standard equation of this function is,

f(x) = 9x² + 2x + 1

We will convert it into the vertex form,

f(x) = 9x² + 2x + 1

    =

    =

    =

    =

    =

    = -------(2)

Vertex of the function →

Equation (1) and (2) are different and both the equations have different vertex.

Therefore, given equation doesn't match the equation given in the vertex form of the function.