To rewrite the function y = x^2 - 4x + 3 in the form y - k = a(x - h)^2, we need to complete the square. Here's how we can do it:
y = x^2 - 4x + 3
First, we need to find the value of h by taking half of the coefficient of x and squaring it. In this case, h = (-4/2)^2 = (-2)^2 = 4.
Next, we subtract and add 4 within the parentheses:
y = (x^2 - 4x + 4 - 4) + 3
Now, we can rewrite the expression within the parentheses as a perfect square:
y = (x^2 - 4x + 4) - 4 + 3
Simplifying further:
y = (x - 2)^2 - 1
Finally, we can compare this expression with the desired form y - k = a(x - h)^2:
y - 1 = 1(x - 2)^2
Therefore, the function y = x^2 - 4x + 3 can be written as y - 1 = 1(x - 2)^2.