To find the zeros and intercepts of the quadratic function $f(x) = 2x^2 - 7x + 5$:

Finding the zeros: Set the function equal to zero, $0 = 2x^2 - 7x + 5$. Factor the trinomial to obtain $(x - 1)(2x - 5) = 0$. Apply the zero product property to solve for $x$, yielding the zeros $x = 1$ and $x = \frac{5}{2}$.

Finding the x-intercepts: Because x-intercepts occur where the function value is zero ($y = 0$), the x-intercepts of the graph are the points $(1, 0)$ and $(\frac{5}{2}, 0)$.

Finding the y-intercepts: To find the y-intercept, evaluate the function at $x = 0$. Substituting $0$ into the function gives $f(0) = 2(0)^2 - 7(0) + 5 = 5$. Thus, the y-intercept is the point $(0, 5)$.