To find the zeros and intercepts of the quadratic function $f(x) = 6x^2 + 13x - 15$:

Finding the zeros: Set the function equal to zero, $0 = 6x^2 + 13x - 15$. Factor the trinomial to obtain $(x + 3)(6x - 5) = 0$. Apply the zero product property to solve for $x$, yielding the zeros $x = -3$ and $x = \frac{5}{6}$.

Finding the x-intercepts: Because x-intercepts occur where the function value is zero ($y = 0$), the x-intercepts of the graph correspond to the zeros. Therefore, the x-intercepts are the points $(-3, 0)$ and $(\frac{5}{6}, 0)$.

Finding the y-intercepts: To find the y-intercept, evaluate the function at $x = 0$. Substituting $0$ into the function gives $f(0) = 6(0)^2 + 13(0) - 15 = -15$. Thus, the y-intercept is the point $(0, -15)$.