Find the vertex, focus, and directrix of the parabola. $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$
A)Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 0$
B)Vertex: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 1$
C)Vertex: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Directrix: $y = 0$
D)Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 1$
E)Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Directrix: $y = 1$

Question

Find the vertex, focus, and directrix of the parabola.  $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$ 
A)Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 0$
B)Vertex: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 1$
C)Vertex: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Directrix: $y = 0$
D)Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 2 \right)$ ; Directrix: $y = 1$
E)Vertex: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Focus: $\left( - \frac { 7 } { 2 } , 1 \right)$ ; Directrix: $y = 1$

Quizplus · Accepted Answer

The given equation $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$ is in the form $(x - h)^2 = 4p(y - k)$, where $(h, k)$ is the vertex of the parabola. Thus, the vertex is $\left( - \frac { 7 } { 2 } , 1 \right)$. The value of $4p = 4$, so $p = 1$, indicating the focus is 1 unit above the vertex, making the focus $\left( - \frac { 7 } { 2 } , 2 \right)$, and the directrix is $y = k - p = 1 - 1 = 0$.

Find the Vertex, Focus, and Directrix of the Parabola (x+72)2=4(y−1)\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )(x+27​)2=4(y−1)

Find the Vertex, Focus, and Directrix of the Parabola $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$