Answer
The x-intercepts are at $(2, 0)$ and $(-\frac{4}{3}, 0)$.
The y-intercept is at $(0, -8)$.
Work Step by Step
To find the x-intercept, you would set f(x) or y = 0:
$0 = 3x2 - 2x - 8$
Now, you solve for x.
First, factor the equation:
$0 = (3x + 4)(x - 2)$
Next, set each factor equal to 0 because for the equation to be equal to zero, one of the factors should be zero:
$3x + 4 = 0$ or $x - 2 = 0$
Now you can solve for x:
$x = 2$
or
$3x = -4$
$x = -\frac{4}{3}$
The x-intercepts are at $(2, 0)$ and $(-\frac{4}{3}, 0)$
To find the y-intercept, you would set x = 0.
$y = 3(0)^{2} - 2(0) - 8$
You then simplify this equation:
$y = 0 - 0 - 8$
You get as your answer:
$y = -8$
The y-intercept is at $(0, -8)$
