Find the vertex, focus, and directrix of the parabola with the given equation.
-$$( y - 4 ) ^ { 2 } = - 16 ( x - 1 )$$
A) vertex: $( 1,4 )$
focus: $( - 3,4 )$
directrix: $x = 5$
B) vertex: $( - 1 , - 4 )$
focus: $( - 5 , - 4 )$
directrix: $x = 3$
C) vertex: $( 1,4 )$
focus: $( 5,4 )$
directrix: $x = - 3$
D) vertex: $( 4,1 )$
focus: $( 0,1 )$
directrix: $x = 8$

Question

Quizplus · Accepted Answer

The given equation is in the form $(y-k)^2 = 4p(x-h)$, where $(h, k)$ is the vertex. Comparing, we find the vertex is $(1, 4)$. The value of $4p = -16$, so $p = -4$, indicating the focus is 4 units to the left of the vertex, making it $(-3, 4)$, and the directrix is a vertical line $x = h + p = 1 + 4 = 5$.

Find the Vertex, Focus, and Directrix of the Parabola with the Given