Find the vertex of the parabola.
-$$f ( x ) = - x ^ { 2 } + 11 x - 3$$

A) $\left( - \frac { 11 } { 2 } , - \frac { 375 } { 4 } \right)$
B) $( 11 , - 3 )$
C) $\left( \frac { 11 } { 2 } , \frac { 133 } { 4 } \right)$
D) $\left( \frac { 11 } { 2 } , \frac { 109 } { 4 } \right)$

Question

Find the vertex of the parabola.
-$$f ( x ) = - x ^ { 2 } + 11 x - 3$$

A) $\left( - \frac { 11 } { 2 } , - \frac { 375 } { 4 } \right)$
B) $( 11 , - 3 )$
C) $\left( \frac { 11 } { 2 } , \frac { 133 } { 4 } \right)$
D) $\left( \frac { 11 } { 2 } , \frac { 109 } { 4 } \right)$

Quizplus · Accepted Answer

The vertex of a parabola in the form $f(x) = ax^2 + bx + c$ is given by $\left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right)$. For $f(x) = -x^2 + 11x - 3$, $a = -1$, $b = 11$. The x-coordinate of the vertex is $-\frac{11}{2(-1)} = \frac{11}{2}$. Substituting $\frac{11}{2}$ into the function gives the y-coordinate $\frac{109}{4}$. Thus, the vertex is $\left( \frac{11}{2}, \frac{109}{4} \right)$.

Find the Vertex of the Parabola f(x)=−x2+11x−3f ( x ) = - x ^ { 2 } + 11 x - 3f(x)=−x2+11x−3

Find the Vertex of the Parabola $f ( x ) = - x ^ { 2 } + 11 x - 3$