The given function is:

$y = \frac{x^3}{4} - 4x + 3$

Step 1: Identify the Leading Term

The leading term in a polynomial is the term with the highest power of $x$. Here, the term with the highest power is:

$\frac{x^3}{4}$

Step 2: Identify the Leading Coefficient

The leading coefficient is the coefficient of the leading term. In this case, the coefficient of $x^3$ is:

$\frac{1}{4}$

Final Answer:

The leading coefficient is $\frac{1}{4}$.

Would you like a deeper explanation or have any questions?

Here are five related questions to expand on this concept:

1. What is the degree of the polynomial $y = \frac{x^3}{4} - 4x + 3$?
2. How do you determine the end behavior of this function?
3. What are the critical points of the function?
4. How does the leading coefficient affect the graph of a polynomial?
5. What happens if the leading coefficient is negative?

Math Tip:

The leading coefficient determines the growth rate and direction of a polynomial function. If it's positive, the right side of the graph goes up; if negative, the right side goes down.