Additional Concepts
-$$x = - ( y + 3 ) ^ { 2 } - 8$$
A) Opens to left; $( - 8 , - 3 )$
B) Opens to left; $( - 8,3 )$
C) Opens to left; $( - 3 , - 8 )$
D) Opens to right; $( - 3 , - 8 )$ Use the vertex and the direction in which the parabola opens to determine the relation's domain and range.

Question

Quizplus · Accepted Answer

The equation is in the form of a parabola that opens to the left because the squared term is negative, indicating a horizontal parabola. The vertex form of a horizontal parabola is $x = a(y - k)^2 + h$, where $(h, k)$ is the vertex. Comparing this to the given equation, $x = -(y + 3)^2 - 8$, we find the vertex to be $(-8, -3)$, confirming the parabola opens to the left with the vertex at $(-8, -3)$.

Additional Concepts - x=−(y+3)2−8x = - ( y + 3 ) ^ { 2 } - 8x=−(y+3)2−8

Additional Concepts
- $x = - ( y + 3 ) ^ { 2 } - 8$