Respuesta :
The x-intercepts are [tex](0,0)[/tex]
The y-intercepts are [tex](0,0),(0,3),(0,-3)[/tex]
Explanation:
The relation is [tex]x=y^{4} -9y^{2}[/tex]
To find the x-intercept, let us substitute [tex]y=0[/tex] in the equation [tex]x=y^{4} -9y^{2}[/tex], we get,
[tex]x=(0)^{4} -9(0)^{2} \\x=0[/tex]
Thus, the x-intercepts are [tex](0,0)[/tex]
To find the y-intercept, let us substitute [tex]x=0[/tex] in the equation [tex]x=y^{4} -9y^{2}[/tex], we get,
[tex]0=y^{4}-9 y^{2}[/tex]
let us switch sides and solving, we get,
[tex]\begin{aligned}y^{4}-9 y^{2} &=0 \\y^{2}\left(y^{2}-9\right) &=0 \\y^{2} &=0, y^{2}-9=0\end{aligned}[/tex]
Taking square root,
[tex]y=0[/tex] and [tex]\begin{aligned}y^{2}-9 &=0 \\y^{2} &=9 \\y &=\pm 3\end{aligned}[/tex]
Thus, the y-intercepts are [tex](0,0),(0,3),(0,-3)[/tex]
