Find the vertex of the graph of the quadratic function.
-$$f ( x ) = - 3 x ^ { 2 } + 6 x + 1$$
A) $( 1,4 )$
B) $( 2 , - 5 )$
C) $( - 1 , - 8 )$
D) $( - 2 , - 23 )$

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 the given function, $a = -3$ and $b = 6$, so the x-coordinate of the vertex is $- \frac{6}{2(-3)} = 1$. Substituting $x = 1$ into the function gives $f(1) = -3(1)^2 + 6(1) + 1 = 4$. Therefore, the vertex is $(1, 4)$.

Find the Vertex of the Graph of the Quadratic Function f(x)=−3x2+6x+1f ( x ) = - 3 x ^ { 2 } + 6 x + 1f(x)=−3x2+6x+1

Find the Vertex of the Graph of the Quadratic Function $f ( x ) = - 3 x ^ { 2 } + 6 x + 1$