The square for y = x^2 - 8x + 12, add (8/2)^2 = 16 to both sides, resulting in y = (x - 4)^2 + 12.
To put the equation y = x^2 - 8x + 12 into the form y = (x - h)^2 + k, we can complete the square.
First, we move the constant term to the left side of the equation:
y - 12 = x^2 - 8x
Next, we can factor the quadratic on the right side of the equation:
y - 12 = (x - 4)^2
Finally, we add 16 to both sides of the equation to isolate y on the left:
y = (x - 4)^2 + 12
Therefore, the equation y = x^2 - 8x + 12 can be written in the form y = (x - h)^2 + k as follows:
y = (x - 4)^2 + 12
where h = 4 and k = 12.
The image shows the equation y = x^2 - 8x + 12 in the form y = (x - h)^2 + k, where h = 4 and k = 12. The graph of the equation is a parabola with vertex at (4, 12).