The function you provided is:

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

It is a quadratic function. Let's explore a few things we can do with it:

1. Find the Vertex of the Parabola

To find the vertex of the parabola represented by this quadratic function, we use the vertex formula:

$x = \frac{-b}{2a}$

where $a = 1$ and $b = -8$ for the given function.

2. Find the Roots (x-intercepts) of the Function

We can use the quadratic formula to find the roots of the function:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Where $a = 1$, $b = -8$, and $c = 12$.

3. Determine the Y-intercept

The y-intercept occurs when $x = 0$. We can substitute $x = 0$ into the function:

$f(0) = 0^2 - 8(0) + 12$

Let me know which part you would like to explore further or if you'd like me to proceed with a specific calculation!

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Follow-up Questions:

1. How do you graph a quadratic function like this?
2. What does the discriminant tell you about the nature of the roots?
3. How do we complete the square for this quadratic?
4. What happens to the graph if you change the values of $a$, $b$, or $c$?
5. How can you solve this quadratic by factoring?

Tip: If the discriminant ($b^2 - 4ac$) is positive, the quadratic has two real roots. If it's zero, there is one real root, and if it's negative, there are no real roots (the roots are complex).