For the graph given, state the location of the vertices, the equation of the transverse axis, the location of the center, and the equation of the conjugate axis. (Gridlines are spaced one unit apart.)
A) vertices: (1, 2), (1, 4); transverse axis: x = 3; center (1, 3); conjugate axis: y = 1
B) vertices: (1, 2), (1, 4); transverse axis: y = 3; center (1, 3); conjugate axis: x = 1
C) vertices: (1, 2), (1, 4); transverse axis: x = 1; center (1, 3); conjugate axis: y = 3
D) vertices: (1, 2), (1, 4); transverse axis: y = 1; center (1, 3); conjugate axis: x = 3

Question

For the graph given, state the location of the vertices, the equation of the transverse axis, the location of the center, and the equation of the conjugate axis.  (Gridlines are spaced one unit apart.)
A) vertices: (1, 2), (1, 4); transverse axis: x = 3; center (1, 3); conjugate axis: y = 1 
B) vertices: (1, 2), (1, 4); transverse axis: y = 3; center (1, 3); conjugate axis: x = 1 
C) vertices: (1, 2), (1, 4); transverse axis: x = 1; center (1, 3); conjugate axis: y = 3 
D) vertices: (1, 2), (1, 4); transverse axis: y = 1; center (1, 3); conjugate axis: x = 3

Quizplus · Accepted Answer

The transverse axis of the graph is horizontal and passes through the points (1,2) and (1,4). This means that the center of the graph must be at (1,3) since that is the midpoint of the vertices.

The length of the transverse axis is the difference in the x-coordinates of the vertices, which is 0. Therefore, the equation of the transverse axis is x=1.

The conjugate axis is vertical and runs through the center, with a length equal to the difference in the y-coordinates of the vertices. This length is 2, so the equation of the conjugate axis is y=3±1. Since the center is at (1,3), the equation of the conjugate axis is y=3±1, or y=2 and y=4.

Therefore, the correct answer is C.

For the Graph Given, State the Location of the Vertices