Find the vertex of the graph of the quadratic function.
-$f ( x ) = - x ^ { 2 } + x - 4$
A) $( 1 , - 4 )$
B) $( - 1 , - 6 )$
C) $\left( - \frac { 1 } { 2 } , - \frac { 19 } { 4 } \right)$
D) $\left( \frac { 1 } { 2 } , - \frac { 15 } { 4 } \right)$

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 $x = -\frac{b}{2a}$. For the given function, $a = -1$ and $b = 1$, so $x = -\frac{1}{2(-1)} = \frac{1}{2}$. Plugging $x = \frac{1}{2}$ back into the function gives $f\left(\frac{1}{2}\right) = -\left(\frac{1}{2}\right)^2 + \frac{1}{2} - 4 = -\frac{1}{4} + \frac{1}{2} - 4 = -\frac{15}{4}$. Therefore, the vertex is $\left(\frac{1}{2}, -\frac{15}{4}\right)$.

Find the Vertex of the Graph of the Quadratic Function f(x)=−x2+x−4f ( x ) = - x ^ { 2 } + x - 4f(x)=−x2+x−4

Find the Vertex of the Graph of the Quadratic Function $f ( x ) = - x ^ { 2 } + x - 4$