Complete the square to re-write the quadratic function in vertex form:y, equals, x, squared, minus, 4, x, plus, 6y=x 2 −4x+6

Sure, let's complete the square to rewrite the quadratic function in vertex form.

Given the quadratic function: $y = x^2 - 4x + 6$

Step 1: Start with the quadratic and linear terms. $y = x^2 - 4x$

Step 2: To complete the square, take the coefficient of $x$, which is $-4$, divide it by 2, and then square it. $\left(\frac{-4}{2}\right)^2 = (-2)^2 = 4$

Step 3: Add and subtract this square inside the equation. $y = x^2 - 4x + 4 - 4 + 6$

Step 4: Group the perfect square trinomial and the constants. $y = (x^2 - 4x + 4) + (-4 + 6)$

Step 5: Rewrite the perfect square trinomial as a binomial squared. $y = (x - 2)^2 + 2$

So, the quadratic function in vertex form is: $y = (x - 2)^2 + 2$