Answer
x-intercepts: -2 and 2
y-intercepts: -4 and 4
Work Step by Step
RECALL:
(i) The x-intercept is the value of x when y=0.
(ii) The y-intercept is the value of y when x=0.
Based on the given graph of the function, it appears that the function has:
x-intercepts: -2 and 2
y-intercepts: -4 and 4
Check if these are the actual intercepts by substituting each one to the given equation:
For x=-2:
$\\(-2)^4+0^2-(-2)(0)=16
\\16+0-0=16
\\16=16$
For x=2:
$\\2^4+0^2-(2)(0)=16
\\16+0-0=16
\\16=16$
Thus, -2 and 2 are x-intercepts of the equation.
For y=-4:
$\\0^4+(-4)^2-(0)(-4)=16
\\0+16-0=16
\\16=16$
For y=4:
$\\0^4+4^2-(0)(4)=16
\\0+16-0=16
\\16=16$
Thus, -4 and 4 are y-intercepts of the equation.