Answer:
f(x) = (x -3)^2 - 1
Step-by-step explanation:
f(x) = x^2 - 6x + 8
a = 1, b = -6 and c = 8
So we are finding half of the b equation (ignore the negative sign)
Half of 6 is 3, so we are going to square 3 (3^2 = 9) and add 9 to the left side and subtract 9 to the right side
(x) = (x^2 - 6x + 9) + (8 - 9)
You can tell the polynomial is a perfect square, so we will have to factor it using the perfect square method
(x^2 - 6x + 9)
square toot of x^2 is x and square root of 9 is 3 and the operation sign after the a number is a minus sign
(x -3)^2
Don't forget the rest of the equation from before
(x -3)^2 + (8 - 9)
(x -3)^2 - 1
So the equation is f(x) = (x -3)^2 - 1
