Question

What is the vertex of the graph of the function below?
y=x2-4x+3
rY.
ry.
O (1,-1)
0 (2,01
0 (1,01
O (2,-1)

Answer 1

To find the vertex of the quadratic function given by \( y = x^2 - 4x + 3 \), we can use the vertex formula for a quadratic function in the form \( y = ax^2 + bx + c \).

The x-coordinate of the vertex can be found using the formula:

\[
x = -\frac{b}{2a}
\]

In this case, \( a = 1 \) and \( b = -4 \):

\[
x = -\frac{-4}{2 \cdot 1} = \frac{4}{2} = 2
\]

Next, we substitute \( x = 2 \) back into the original function to find the y-coordinate of the vertex:

\[
y = (2)^2 - 4(2) + 3
\]
\[
y = 4 - 8 + 3
\]
\[
y = -1
\]

Thus, the vertex of the graph \( y = x^2 - 4x + 3 \) is at the point:

\[
(2, -1)
\]

So the correct answer is:

**O (2, -1)**.