Find the vertex of the parabola.
-$$h ( x ) = - 2 x ^ { 2 } + 12 x - 19$$
A) $( - 3 , - 1 )$
B) $( - 1 , - 3 )$
C) $( 0 , - 19 )$
D) $( 3 , - 1 )$

Question

Quizplus · Accepted Answer

The vertex of a parabola in the form $h(x) = ax^2 + bx + c$ can be found using the formula $(-\frac{b}{2a}, h(-\frac{b}{2a}))$. For $h(x) = -2x^2 + 12x - 19$, $a = -2$, $b = 12$, so the x-coordinate of the vertex is $-\frac{12}{2(-2)} = 3$. Plugging $x = 3$ back into the equation gives $h(3) = -2(3)^2 + 12(3) - 19 = -18 + 36 - 19 = -1$. Therefore, the vertex is $(3, -1)$.

Find the Vertex of the Parabola h(x)=−2x2+12x−19h ( x ) = - 2 x ^ { 2 } + 12 x - 19h(x)=−2x2+12x−19

Find the Vertex of the Parabola $h ( x ) = - 2 x ^ { 2 } + 12 x - 19$