Answer
x-intercepts at (3,0) and (-3,0)
y-intercept at (0,9)
symmetric to y-axis
Work Step by Step
Find Intercepts:
x-int
0=9-$x^{2}$
x=3,-3
x-intercepts at (3,0) and (-3,0)
y-int
y=9-$0^{2}$
y=9
y-intercept at (0,9)
Find Symmetry:
Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis.
y=9-$(-x)^{2}$
y=9-$x^{2}$
Equations are equivalent, so function is symmetric to y-axis.
Substitute -y for y. If equation is equivalent, graph is symmetric to x-axis.
(-y)=9-$x^{2}$
y=$x^{2}$-9
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)=9-$(-x)^{2}$
y=$x^{2}$-9
Equations are not equivalent, so not symmetric to origin.
