The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$x ^ { 2 } = - 28 y$$
A) focus: $( 0 , - 7 )$
directrix: $y = 7$
B) focus: $( - 14,0 )$
directrix: $x = 7$
C) focus: $( 0 , - 7 )$
directrix: $y = -7$
D) focus: $( 0,7 )$
directrix: $y = -7$

Question

The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$x ^ { 2 } = - 28 y$$
A) focus: $( 0 , - 7 )$
 directrix: $y = 7$
B) focus: $( - 14,0 )$
directrix: $x = 7$
C) focus: $( 0 , - 7 )$
 directrix: $y = -7$
D) focus: $( 0,7 )$ 
 directrix: $y = -7$

Quizplus · Accepted Answer

The equation $x^2 = -28y$ represents a parabola that opens downwards. The focus of such a parabola is located at $(0, -\frac{1}{4}a)$, where $a$ is the coefficient of $y$ in the equation, making $a = -28$. Thus, the focus is at $(0, -7)$. The directrix is a line parallel to the x-axis, located the same distance from the vertex as the focus but in the opposite direction, making it $y = 7$.

The Parabola 1 Graph Parabolas with Vertices at the Origin x2=−28yx ^ { 2 } = - 28 yx2=−28y

The Parabola
1 Graph Parabolas with Vertices at the Origin $x ^ { 2 } = - 28 y$