Use the vertex and the direction in which the parabola opens to determine the relation's domain and range.
-$y ^ { 2 } - 12 y - x + 38 = 0$
A) Domain: $( 2 , \infty ]$
Range: $( - \infty , \infty )$
B) Domain: $( - \infty , - 2 )$
Range: $( - \infty , \infty )$
C) Domain: $( - \infty , \infty )$
Range: $( - \infty , \infty )$
D) Domain: $( - \infty , \infty )$
Range: $( - \infty , - 2 ]$

Question

Quizplus · Accepted Answer

The given equation can be rewritten as $(y-6)^2 = x-2$, which is the standard form of a parabolic equation with the vertex at $(2,6)$ and the direction opening rightward. The domain is therefore $(2,\infty]$ since the parabola only extends to the right. The range is $(-\infty,\infty)$ since the parabola extends infinitely up and down. Choice A is the only option that matches these characteristics.

Use the Vertex and the Direction in Which the Parabola y2−12y−x+38=0y ^ { 2 } - 12 y - x + 38 = 0y2−12y−x+38=0

Use the Vertex and the Direction in Which the Parabola $y ^ { 2 } - 12 y - x + 38 = 0$