Identify the coordinates of the vertex and focus, the equations of the axis of
symmetry and directrix, and the direction of opening of the parabola with the equation . Then find the length of the latus rectum and graph the parabola.

a.

The coordinates of the vertex and focus are (–5, 2) and (,
2) respectively. The equations of the axis of symmetry and directrix are x = –5 and
x = respectively. The direction of the opening
is right and the length of the latus rectum is units. The graph of the
parabola is as follows:

c.

The coordinates of the vertex and
focus are (–5, 2) and (2, ) respectively. The equations of the axis of
symmetry and directrix are and x =
respectively. The direction of the opening is right and the length of the latus rectum is units. The graph of the parabola is as follows:

b.

The coordinates of the vertex and focus are (–5, 2) and (,
2) respectively. The equations of the axis of symmetry and directrix are
and x = respectively. The direction of the opening
is right and the length of the latus rectum is units. The graph of the
parabola is as follows:

d.

The coordinates of the vertex and focus are
(–5, 2) and (, 2) respectively. The equations of the axis
of symmetry and directrix are and x =
respectively. The direction of the opening is left and the length of the latus rectum is units. The graph of the parabola is as follows:

Identify the coordinates of the vertex and focus, the equations of the axis of
symmetry and directrix, and the direction of opening of the parabola with the equation y =
6x^{2} + 24x + 18. Then find the length of the latus rectum and graph the
parabola.

a.

The coordinates of the vertex and focus are (2, –6) and (2, )
respectively. The equations of the axis of symmetry and directrix are and y =
respectively. The direction of the opening
is upward, and the length of the latus rectum is units. Thus, the graph of
the parabola is as follows:

c.

The coordinates of the vertex and
focus are (2, –6) and (2, ) respectively. The equations of the axis of
symmetry and directrix are and y =
respectively. The direction of opening is downward, and the length of the latus rectum is units. Thus, the graph of the parabola is as follows:

b.

The coordinates of the vertex and focus are (–2, –6) and (–2, ) respectively. The equations of the axis of symmetry and directrix are y =
–6 and y = respectively. The direction of opening is
upward, and the length of the latus rectum is units. Thus, the graph of the
parabola is as follows:

d.

The coordinates of the vertex and focus are
(–2, –6) and (–2, ) respectively. The equations of the axis of
symmetry and directrix are and y =
respectively. The direction of opening is upward, and the length of the latus rectum is units. Thus, the graph of the parabola is as follows: