Answer
No symmetry
x-intercepts at (0,0) and (-5,0)
y-intercept at (0,0)
Work Step by Step
Find Intercepts:
x-int
0=x$\sqrt (x+5)$
x=0,-5
x-intercepts at (0,0) and (-5,0)
y-int
y=(0)$\sqrt (0+5)$
y=0
y-intercept at (0,0)
Find Symmetry:
Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis.
y=(-x)$\sqrt ((-x)+5)$
y=-x$\sqrt (5-x)$
Equations are not equivalent, so not symmetric to y-axis.
Substitute -y for y. If equation is equivalent, graph is symmetric to x-axis.
(-y)=x$\sqrt (x+5)$
y=-x$\sqrt (x+5)$
Equations are not equivalent, so not symmetric to x-axis.
Substitute -y for y and -x for x. If equation is equivalent, graph is symmetric to origin.
(-y)=(-x)$\sqrt ((-x)+5)$
y=x$\sqrt (5-x)$
Equations are not equivalent, so not symmetric to origin.
