Answer
$x$-Intercept: $9$
$y$-intercepts: $-3$ and $3$
The graph is symmetric with respect to the $x$-axis.
Work Step by Step
To find the $x$-intercept/s of the graph of an equation, you set $y = 0$ and then solve fpor $x$.
To find the $y$-intercept/s of the graph of an equation, you set $x = 0$ and then solve for $y$..
To find the $y$-intercepts, set $x=0$ to obtain:
$y^{2} = 0+9\\
y^2=9\\
\sqrt{y^2}=\pm\sqrt9\\
y=\pm3$
To find the $x$-intercepts, set $y=0$ to obtain:
$0^2 = x + 9\\
0=x+9\\
0-9=x\\
-9=x$.
To check for symmetry about the $x$-axis, replace $y$ with $-y$ in the original equation.
If the resuting equation is equivalent to the original, then the graph is symmetric with respect to the $x$-axis.
Replace $y$ with $-y$ to obtain:
$(-y)^{2} = x +9\\
y^2=x+9$
Since the resulting equation is the same as the original, then the graph is symmetric with respect to the $x$-axis.
To check for symmetry about the $y$-axis, replace $x$ with $-x$ in the original equation
If the resulting equation is eqivalent to the original, then the graph is symmetric with respect to the $y$-axis
Replace $x$ with $-x$ to obtain:
$y^{2} = -x+9$
This equation is different from the original so the graph is not symmetric with respect to the $y$=axis.
To check for symmetry with respect to the origin, replace $x$ with $-x$ and $y$ with $-y$ in the original equation.
If the resulting equation is equivalent to the original, then the graph is symmetric with respect to the $y$-axis
Replace $x$ with $-x$ and $y$ wtith $-y$ to obtain:
$(-y)^2 = -x+9\\
y^2=-x+9$
This equation is different from the original so the graph is not symmetric with respect to the origin.
