Question

What is the vertex of the graph of y = 1/3 (x-9)2 + 5 Question 1 options: (9,5) (3,3) (3,5) (-9,5)

Answer 1

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

Answer 2

ANSWER

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

$(9,5)$



EXPLANATION

The vertex form of a parabola is given by

$y = a {(x - h)}^{2} + k$

where
$V(h,k)$
is the vertex of the parabola.


The function given to us is

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


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

$a = \frac{1}{3}$

$h = 9$
and

$k = 5$


Therefore the vertex of the parabola is

$V(9,5)$

Hence the correct answer is option A.