To find $f(-5)$ for the function $f(x) = 4x^2 - 12x + 1$, follow these steps:

1. Substitute $x = -5$ into the given function: $f(-5) = 4(-5)^2 - 12(-5) + 1$

2. Simplify the expression: $= 4(25) + 60 + 1$ $= 100 + 60 + 1$

3. Add the terms: $f(-5) = 161$

Thus, $f(-5) = 161$.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How would you find the vertex of the quadratic function $f(x) = 4x^2 - 12x + 1$?
2. What is the discriminant of the quadratic function, and how does it determine the number of real roots?
3. How would you solve $f(x) = 0$ for this quadratic function?
4. How can you express $f(x)$ in vertex form?
5. What is the axis of symmetry for the function $f(x)$?

Tip: In any quadratic function $f(x) = ax^2 + bx + c$, the axis of symmetry can be found using the formula $x = -\frac{b}{2a}$.