Respuesta :

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\ -------------------------------\\\\ y=\cfrac{1}{3}(x-\stackrel{h}{9})^2+\stackrel{k}{5}\qquad \qquad vertex~(9,5)[/tex]
kudzordzifrancis
ANSWER

The vertex of the graph of
[tex]y = \frac{1}{3} {(x - 9)}^{2} + 5[/tex]
is

[tex](9,5)[/tex]



EXPLANATION

The vertex form of a parabola is given by

[tex]y = a {(x - h)}^{2} + k[/tex]

where
[tex]V(h,k)[/tex]
is the vertex of the parabola.


The function given to us is

[tex]y = \frac{1}{3} {(x - 9)}^{2} + 5 [/tex]
This is already in the vertex form.


When we compare this to the general vertex form, we have,

[tex]a = \frac{1}{3} [/tex]

[tex]h = 9[/tex]
and

[tex]k = 5[/tex]


Therefore the vertex of the parabola is

[tex]V(9,5)[/tex]

Hence the correct answer is option A.

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