Answer
x-intercepts at ($\frac{-1}{2}$,0) and (0,0)
y-intercept at (0,0)
no symmetry
Work Step by Step
Find Intercepts:
x-int
0=2$x^{2}$+x
0=x(2x+1)
x=$\frac{-1}{2}$,0
x-intercepts at ($\frac{-1}{2}$,0) and (0,0)
y-int
y=2$(0)^{2}$+0
y=0
y-intercept at (0,0)
Find Symmetry:
Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis.
y=2$(-x)^{2}$+(-x)
y=2$x^{2}$-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)=2$x^{2}$+x
y=-2$x^{2}$-x
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)=2$(-x)^{2}$+(-x)
y=x-2$x^{2}$
Equations are not equivalent, so not symmetric to origin.
