Answer
$x$-intercepts $=0,-3$
$y$-intercept $=0$
Work Step by Step
$y=\dfrac{x^{2}+3x}{(3x+1)^{2}}$
Find the $y$-intercept by setting $x$ equal to zero and solving for $y$:
$x=0$
$y=\dfrac{(0)^{2}+3(0)}{[3(0)+1]^{2}}=\dfrac{0+0}{(0+1)^{2}}=\dfrac{0}{1}=0$
$y$-intercept $=0$
Find the $x$-intercept by setting $y$ equal to zero and solving for $x$:
$y=0$
$0=\dfrac{x^{2}+3x}{(3x+1)^{2}}$
$(0)(3x+1)^{2}=x^{2}+3x$
$x^{2}+3x=0$
$x(x+3)=0$
$x=0$
$x+3=0$
$x=-3$
$x$-intercepts $=0,-3$
