Chapter P - P.1 - Graphs and Models - Exercises: 42

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.

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