Answer
The $y$-intercept is $-8$.
The $x$-intercepts are $-\dfrac{4}{3}$ and $2$.
Work Step by Step
Determine the $y$-intercept by setting $x=0$ then solving for $y$:
$y=f(0)=3(0^2)-2(0)-8=-8$
Thus, the $y$-intercept is $-8$.
Determine the $x$-intercepts by sestting $y=0$ then solving the equation using the quadratic formula $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$.
$3x^2-2x-8=0$ (so $a=3, b=-2,$ and $c=-8$)
$x=\dfrac{2\pm\sqrt{(-2)^2-4(3)(-8)}}{2(3)}=\dfrac{2\pm 10}{6}=\dfrac{1\pm 5}{3}$
$x_1=\dfrac{1-5}{3}=-\dfrac{4}{3}$
$x_2=\dfrac{1+5}{3}=2$
Thus, the $x$-intercepts are $-\dfrac{4}{3},2$.
