Answer:
Step-by-step explanation:
Given function in the vertex form is,
f(x) = (3x + 13)² + 89
= [tex]9(x+\frac{13}{3})^{2}+89[/tex] --------(1)
Vertex of the parabola → [tex](-\frac{13}{3},89)[/tex]
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
= [tex]9(x^{2}+\frac{2}{9}x)+1[/tex]
= [tex]9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}-(\frac{1}{9})^2]+1[/tex]
= [tex]9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}]-9(\frac{1}{9})^2+1[/tex]
= [tex]9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}]-(\frac{1}{9})+1[/tex]
= [tex]9(x+\frac{1}{9})^2+\frac{9-1}{9}[/tex]
= [tex]9(x+\frac{1}{9})^2+\frac{8}{9}[/tex] -------(2)
Vertex of the function → [tex](-\frac{1}{9},\frac{8}{9})[/tex]
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.
