The given function is:

$f(x) = x^2 - 8x - 12$

This is a quadratic function because it is a polynomial of degree 2. A quadratic function can generally be written as:

$f(x) = ax^2 + bx + c$

where:

• $a$, $b$, and $c$ are constants, and
• the highest power of $x$ is 2.

In this case:

• $a = 1$ (since the coefficient of $x^2$ is 1),
• $b = -8$ (the coefficient of $x$),
• $c = -12$ (the constant term).

Key Characteristics:

• The graph of this function is a parabola.
• Since $a = 1 > 0$, the parabola opens upward.
• The vertex of the parabola gives the minimum value of the function.

Would you like to explore how to find the vertex or other properties of this function?

Related Questions:

1. How do you find the vertex of a quadratic function?
2. What is the axis of symmetry for this quadratic function?
3. How do you find the roots of a quadratic equation?
4. What is the discriminant of a quadratic function, and what does it tell us?
5. How can you graph a quadratic function step-by-step?

Tip: You can rewrite the quadratic function in vertex form by completing the square to find the vertex directly.