Find the vertex and focus of the parabola.
A)vertex: focus:
B)vertex: focus:
C)vertex: focus:
D)vertex: focus:
E)vertex: focus:

Question

Find the vertex and focus of the parabola. 
A)vertex: focus: 
B)vertex: focus: 
C)vertex: focus: 
D)vertex: focus: 
E)vertex: focus:

Quizplus · Accepted Answer

Since the parabola opens upwards, we know the vertex is the lowest point on the parabola. Therefore, the vertex is at (7,-6). 
The focus is also above the vertex and is located along the axis of symmetry. The distance from the vertex to the focus is given by the equation $a=\frac{1}{4p}$, where $p$ is the distance from the vertex to the directrix. We see that $4p=8$, so $p=2$ and $a=\frac{1}{8}$. Therefore, the focus is located $\frac{1}{8}$ units above the vertex at (7,-$\frac{47}{8}$). 
Option D matches these values, so it is the correct choice.

Find the Vertex and Focus of the Parabola