Here's the graph of the quadratic function $f(x) = x^2 - 4x + 3$. You can observe the minimum point at $x = 2$, where $f(2) = -1$. The table of values and graph illustrate how the function behaves over a range of $x$ values.

Table of Values:

$x$	$f(x) = x^2 - 4x + 3$
$0$	$f(0) = 3$
$1$	$f(1) = 0$
$2$	$f(2) = -1$
$3$	$f(3) = 0$
$4$	$f(4) = 3$

This function is a downward-facing parabola, with a minimum value at $x = 2$.

Do you need more details or have any questions?

5 Related Questions:

1. How do we determine the vertex of any quadratic function?
2. How does changing the coefficients in a quadratic function affect its shape?
3. What is the significance of the discriminant in a quadratic equation?
4. How can we apply this function to real-world optimization problems?
5. What happens when we shift or scale this quadratic function?

Tip:

For any quadratic function $ax^2 + bx + c$, the vertex occurs at $x = -\frac{b}{2a}$, and this point gives either the maximum or minimum value of the function, depending on the sign of $a$.