Find the vertex of the graph of the quadratic function.
-$f ( x ) = - x ^ { 2 } - 12 x + 1$
A) $( - 6,37 )$
B) $( - 12,1 )$
C) $( 6 , - 107 )$
D) $( 6 , - 35 )$

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 $f(x) = -x^2 - 12x + 1$, $a = -1$, $b = -12$, and $c = 1$. Thus, the x-coordinate of the vertex is $- \frac{-12}{2(-1)} = -6$. Substituting $x = -6$ into the function gives $f(-6) = -(-6)^2 - 12(-6) + 1 = -36 + 72 + 1 = 37$. Therefore, the vertex is $(-6, 37)$.

Find the Vertex of the Graph of the Quadratic Function f(x)=−x2−12x+1f ( x ) = - x ^ { 2 } - 12 x + 1f(x)=−x2−12x+1

Find the Vertex of the Graph of the Quadratic Function $f ( x ) = - x ^ { 2 } - 12 x + 1$