Answer:
y = (x-2)² + 2
Step-by-step explanation:
Converting y = x² - 4x + 6 in vertex form simply means converting from standard form y = ax² - bx + c to the vertex form y = a(x-h)² + k
To start always check and make sure your a=1
In this equation our a=1
Next is to find (b/2)²
(b/2)² = (-4/2)² = (-2)² = 4
Now we want to create a perfect square in our given equation, to do that we will add the value of (b/2)² which is equal to 4 to the linear and quadratic term. That is;
y = x² - 4x + 6
y =( x² - 4x + 4) + 6
Since we added 4 into the parenthesis, we will subtract 4 outside the parenthesis to normalize the equation
y = (x² - 4x + 4) + 6 -4
We now have y = (x² - 4x + 4) + 2 ---------(1)
In the parenthesis we have: x² - 4x + 4 and this is a perfect square, think of the square that will give you this result, and that square is (x-2)²
We will now replace x² - 4x + 4 by (x-2)² in equation (1)
y = (x-2)² + 2
Therefore y = x2 - 4x + 6 in vertex form is y = (x-2)² + 2
