Graph Parabolas with Vertices Not at the Origin
-$$( x + 2 ) ^ { 2 } = 8 ( y - 3 )$$
A) vertex: $( - 2,3 )$
focus: $( - 2,5 )$
directrix: $y = 1$
B) vertex: $( 2 , - 3 )$
focus: $( 2 , - 1 )$
directrix: $y = - 5$
C) vertex: $( 3 , - 2 )$
focus: $( 3,0 )$
directrix: $y = - 4$
D) vertex: $( - 2,3 )$
focus: $( - 2,1 )$
directrix: $x = 5$

Question

Quizplus · Accepted Answer

The equation $(x + 2)^2 = 8(y - 3)$ is in the form $(x - h)^2 = 4p(y - k)$, where $(h, k)$ is the vertex. Thus, the vertex is $(-2, 3)$. The value of $4p = 8$, so $p = 2$, indicating the focus is 2 units above the vertex (since $p$ is positive and the parabola opens upwards), making the focus $(-2, 3 + 2) = (-2, 5)$. The directrix is a horizontal line $p$ units below the vertex, so $y = 3 - 2 = 1$.

Graph Parabolas with Vertices Not at the Origin - (x+2)2=8(y−3)( x + 2 ) ^ { 2 } = 8 ( y - 3 )(x+2)2=8(y−3)

Graph Parabolas with Vertices Not at the Origin
- $( x + 2 ) ^ { 2 } = 8 ( y - 3 )$