To determine the $y$-intercept of the function $y = x^2 - 15x + 10$, we set $x = 0$ because the $y$-intercept occurs where the graph intersects the $y$-axis, and at this point, $x = 0$.

Substitute $x = 0$ into the equation:

$y = 0^2 - 15(0) + 10$

$y = 10$

Thus, the coordinates of the $y$-intercept are:

$(0, 10)$

Would you like more details or additional questions on this topic? Here are some related questions for further exploration:

1. How do you find the $x$-intercepts of the function $y = x^2 - 15x + 10$?
2. Can you rewrite $y = x^2 - 15x + 10$ in vertex form and identify its vertex?
3. What is the axis of symmetry for this quadratic function?
4. How do you determine whether the parabola opens upward or downward?
5. How can you calculate the minimum or maximum value of this quadratic function?

Tip: For quadratic functions, the $y$-intercept is always given by the constant term when the equation is in standard form $ax^2 + bx + c$.