What is the vertex of the graph of the function below? y=x^2-4x+3 A. (1,0) B. (1,-1) C. (2,-1) D. (2,0)

To find the vertex of the quadratic function $y = x^2 - 4x + 3$, we can use the vertex formula for a parabola in the form $y = ax^2 + bx + c$, which is given by:<br /><br />\[ x = -\frac{b}{2a} \]<br /><br />For the given function $y = x^2 - 4x + 3$, we have:<br />- $a = 1$<br />- $b = -4$<br />- $c = 3$<br /><br />Plugging these values into the vertex formula, we get:<br /><br />\[ x = -\frac{-4}{2 \cdot 1} = \frac{4}{2} = 2 \]<br /><br />Now, substitute $x = 2$ back into the original function to find the corresponding $y$-coordinate:<br /><br />\[ y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1 \]<br /><br />Therefore, the vertex of the graph of the function $y = x^2 - 4x + 3$ is $(2, -1)$.<br /><br />The correct answer is:<br />C. $(2, -1)$