Find the vertex of the parabola.
-$$f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } + 9 x - 3$$
A) $( 27 , - 3 )$
B) $\left( \frac { 27 } { 2 } , \frac { 231 } { 4 } \right)$
C) $( - 27 , - 489 )$
D) $\left( - \frac { 27 } { 2 } , - \frac { 741 } { 4 } \right)$

Question

Quizplus · Accepted Answer

The vertex of a parabola in the form $f(x) = ax^2 + bx + c$ can be found using the formula $x = -\frac{b}{2a}$. For the given function, $a = -\frac{1}{3}$ and $b = 9$, so the x-coordinate of the vertex is $x = -\frac{9}{2(-1/3)} = \frac{27}{2}$. Plugging this back into the original equation to find the y-coordinate, $f\left(\frac{27}{2}\right) = -\frac{1}{3}\left(\frac{27}{2}\right)^2 + 9\left(\frac{27}{2}\right) - 3 = \frac{231}{4}$. Therefore, the vertex is $\left(\frac{27}{2}, \frac{231}{4}\right)$.

Find the Vertex of the Parabola f(x)=−13x2+9x−3f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } + 9 x - 3f(x)=−31​x2+9x−3

Find the Vertex of the Parabola $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } + 9 x - 3$