Find the vertex, focus, and directrix of the parabola. $( x + 3 ) + ( y - 1 ) ^ { 2 } = 0$
A)Vertex: $( - 3,1 )$ ; Focus: $\left( \frac { - 13 } { 4 } , 1 \right)$ ; Directrix: $x = \frac { - 11 } { 4 }$
B)Vertex: $( 1 , - 3 , )$ ; Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$
C)Vertex: $( 1 , - 3 , )$ ; Focus: $\left( \frac { - 11 } { 4 } , 1 \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$
D)Vertex: $( - 3,1 )$ ; Focus: $\left( 1 , \frac { - 13 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$
E)Vertex: $( - 3,1 )$ ; Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$

Question

Find the vertex, focus, and directrix of the parabola.  $( x + 3 ) + ( y - 1 ) ^ { 2 } = 0$ 
A)Vertex: $( - 3,1 )$ ; Focus: $\left( \frac { - 13 } { 4 } , 1 \right)$ ; Directrix: $x = \frac { - 11 } { 4 }$
B)Vertex: $( 1 , - 3 , )$ ; Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$
C)Vertex: $( 1 , - 3 , )$ ; Focus: $\left( \frac { - 11 } { 4 } , 1 \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$
D)Vertex: $( - 3,1 )$ ; Focus: $\left( 1 , \frac { - 13 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$
E)Vertex: $( - 3,1 )$ ; Focus: $\left( 1 , \frac { - 11 } { 4 } \right)$ ; Directrix: $x = \frac { - 13 } { 4 }$

Quizplus · Accepted Answer

The correct equation of the parabola should be $(x + 3)^2 + (y - 1)^2 = 0$, which seems to be a mistake in the question as it doesn't describe a parabola. Assuming the intended equation is $y = (x + 3)^2 + 1$, the vertex is at $(-3, 1)$. However, without a correct parabolic equation, determining the focus and directrix accurately is challenging. Given the options and common conventions for parabolas opening upwards or downwards, the vertex at $(-3, 1)$ suggests a horizontal shift left by 3 units and a vertical shift up by 1 unit from the origin, which matches option A's vertex. The focus and directrix provided in option A are plausible if we assume a standard form equation was intended but incorrectly presented.

Find the Vertex, Focus, and Directrix of the Parabola (x+3)+(y−1)2=0( x + 3 ) + ( y - 1 ) ^ { 2 } = 0(x+3)+(y−1)2=0

Find the Vertex, Focus, and Directrix of the Parabola $( x + 3 ) + ( y - 1 ) ^ { 2 } = 0$