Find the vertex of the graph of the quadratic function. $- x ^ { 2 } + 12 x - 36$
A) $( 6,0 )$
B) $( - 6,6 )$
C) $( - 6,0 )$
D) $( 0,6 )$
E) $( - 6 , - 6 )$

Question

Find the vertex of the graph of the quadratic function.   $- x ^ { 2 } + 12 x - 36$  
A) $( 6,0 )$
B) $( - 6,6 )$
C) $( - 6,0 )$
D) $( 0,6 )$
E) $( - 6 , - 6 )$

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 $-x^2 + 12x - 36$, $a = -1$ and $b = 12$, so the x-coordinate of the vertex is $x = -\frac{12}{2(-1)} = 6$. To find the y-coordinate, substitute $x = 6$ into the original equation: $-6^2 + 12(6) - 36 = -36 + 72 - 36 = 0$. Therefore, the vertex is $(6, 0)$.

Find the Vertex of the Graph of the Quadratic Function −x2+12x−36- x ^ { 2 } + 12 x - 36−x2+12x−36

Find the Vertex of the Graph of the Quadratic Function $- x ^ { 2 } + 12 x - 36$