Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. $$g ( x ) = - 4 ( x - 3 ) ^ { 2 } + 12$$
A) (3, 12); minimum
B) (-3, 12); maximum
C) (3, 12); maximum
D) (12, 3); minimum

Question

Quizplus · Accepted Answer

The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For the given function $g(x) = -4(x - 3)^2 + 12$, the vertex is $(3, 12)$. Since the coefficient of the squared term is negative ($a = -4$), the parabola opens downwards, making the vertex a maximum point.

Write the Coordinates of the Vertex and Determine If the Vertex