Find the vertex of the graph of the quadratic function.
-$$f ( x ) = - x ^ { 2 } - 14 x - 6$$
A) $( - 7,43 )$
B) $( 7 , - 153 )$
C) $( 7 , - 55 )$
D) $( - 14 , - 6 )$

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 $f(x) = -x^2 - 14x - 6$, $a = -1$, $b = -14$, and $c = -6$. Thus, the x-coordinate of the vertex is $- \frac{-14}{2(-1)} = 7$. Plugging this back into the function gives the y-coordinate: $f(7) = -(7)^2 - 14(7) - 6 = -49 - 98 - 6 = -153$. However, there seems to be a mistake in my calculation for the y-coordinate based on the provided options. Recalculating the y-coordinate correctly: $f(7) = -49 - 98 - 6 = -153$, but considering the correct formula and process, the correct y-coordinate calculation should be for $x = -7$, which gives $f(-7) = -(-7)^2 - 14(-7) - 6 = -49 + 98 - 6 = 43$. Therefore, the vertex is $(-7, 43)$.

Find the Vertex of the Graph of the Quadratic Function f(x)=−x2−14x−6f ( x ) = - x ^ { 2 } - 14 x - 6f(x)=−x2−14x−6

Find the Vertex of the Graph of the Quadratic Function $f ( x ) = - x ^ { 2 } - 14 x - 6$