Identify the vertex of the parabola.
-$$y = 3 x ^ { 2 } + 12 x + 17$$
A) $( 5 , - 2 )$
B) $( - 5,2 )$
C) $( 2 , - 5 )$
D) $( - 2,5 )$

Question

Quizplus · Accepted Answer

The vertex of a parabola in the form $y = ax^2 + bx + c$ can be found using the formula $(-b/2a, f(-b/2a))$. Here, $a = 3$, $b = 12$, so $-b/2a = -12/(2*3) = -2$. Plugging $-2$ back into the original equation gives $y = 3(-2)^2 + 12(-2) + 17 = 12 - 24 + 17 = 5$. Thus, the vertex is $(-2, 5)$.

Identify the Vertex of the Parabola y=3x2+12x+17y = 3 x ^ { 2 } + 12 x + 17y=3x2+12x+17

Identify the Vertex of the Parabola $y = 3 x ^ { 2 } + 12 x + 17$