Find the vertex of the graph of the quadratic function.
-$f ( x ) = - 6 x ^ { 2 } + 12 x + 9$
A) $( 1,15 )$
B) $( - 2 , - 39 )$
C) $( 2 , - 3 )$
D) $( - 1 , - 9 )$

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, $a = -6$ and $b = 12$, so $x = -\frac{12}{2(-6)} = 1$. To find the y-coordinate of the vertex, substitute $x = 1$ into the original equation: $f(1) = -6(1)^2 + 12(1) + 9 = 15$. Therefore, the vertex is $(1, 15)$.

Find the Vertex of the Graph of the Quadratic Function f(x)=−6x2+12x+9f ( x ) = - 6 x ^ { 2 } + 12 x + 9f(x)=−6x2+12x+9

Find the Vertex of the Graph of the Quadratic Function $f ( x ) = - 6 x ^ { 2 } + 12 x + 9$