Answer
Intercepts are$ y =-2, y =2, x =-4$;
The graph is symmetric about the x-axis.
Work Step by Step
To find the x-intercept of an equation, you set y = 0 and solve, and to find the y-intercept of an equation, you must set x = 0 and solve.
To find the y-intercepts, we use the expression $y^{2} = 4$.
Taking the square root of both sides, $y = 2$ or $y = -2$.
To find the x-intercepts, we use the expression $0 = x + 4$, and therefore, $x = -4$.
To check for symmetry about the x-axis, replace every instance of y with -y in the original equation. The new equation must be equivalent to the original.
Since $(-y)^{2} = x +4$ is the same as $y^{2} = x+4$, there is symmetry about the x-axis.
For symmetry about the y-axis, replace every instance of x with -x.
Since $y^{2} = x+4$ is not the same as $y^{2} = -x+4$, there is no symmetry about the y-axis.
