The equation provided is $y = x^2 - 4x + 3$, which is a quadratic equation. To find the vertex of this quadratic function, we can use the vertex formula for a quadratic equation in the form $y = ax^2 + bx + c$, where the x-coordinate of the vertex is given by:

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

For the equation $y = x^2 - 4x + 3$, we have:

• $a = 1$
• $b = -4$

Substituting these values into the vertex formula:

$x = \frac{-(-4)}{2(1)} = \frac{4}{2} = 2$

Now that we have $x = 2$, we substitute this back into the equation to find the y-coordinate of the vertex:

$y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1$

Thus, the vertex of the quadratic function is $(2, -1)$.

The correct answer is D. (2, -1).

Would you like a detailed explanation of how this process works or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you complete the square to find the vertex of a quadratic equation?
2. What are the effects of changing the value of $a$ in a quadratic equation?
3. How can you identify the axis of symmetry from a quadratic equation?
4. What is the discriminant, and how does it relate to the vertex and roots of a quadratic?
5. How do you find the focus and directrix of a quadratic function?

Tip: The vertex form of a quadratic equation, $y = a(x-h)^2 + k$, makes identifying the vertex $(h, k)$ much easier than the standard form.