Find the vertex of the graph of the quadratic function.
-$f ( x ) = x ^ { 2 } - 11 x - 7$
A) $( 13 , - 7 )$
B) $( - 11,235 )$
C) $\left[ - \frac { 11 } { 2 } , \frac { 335 } { 4 } \right]$
D) $\left( \frac { 11 } { 2 } , - \frac { 149 } { 4 } \right)$

Question

Quizplus · Accepted Answer

The vertex of a quadratic function in the form $f(x) = ax^2 + bx + c$ can be found using the formula $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. For $f(x) = x^2 - 11x - 7$, $a = 1$, $b = -11$, and $c = -7$. Thus, the x-coordinate of the vertex is $- \frac{-11}{2(1)} = \frac{11}{2}$. Substituting $\frac{11}{2}$ back into the function gives the y-coordinate: $f(\frac{11}{2}) = (\frac{11}{2})^2 - 11(\frac{11}{2}) - 7 = -\frac{149}{4}$. Therefore, the vertex is $\left( \frac{11}{2}, -\frac{149}{4} \right)$.

Find the Vertex of the Graph of the Quadratic Function f(x)=x2−11x−7f ( x ) = x ^ { 2 } - 11 x - 7f(x)=x2−11x−7

Find the Vertex of the Graph of the Quadratic Function $f ( x ) = x ^ { 2 } - 11 x - 7$