Complete the Square
f(x)= -x^2+2x
To complete the square for the given quadratic function f(x) = -x^2 + 2x, follow these steps:
Step 1: Group the x-terms together:
f(x) = (-x^2 + 2x)
Step 2: Divide the coefficient of the x-term by 2 and square it:
b = 2/2 = 1
c = (1)^2 = 1
Step 3: Add and subtract the value obtained in step 2 inside the parentheses:
f(x) = (-x^2 + 2x + 1 - 1)
Step 4: Rearrange the terms:
f(x) = (-(x^2 - 2x + 1) - 1)
Step 5: Rewrite the expression inside the parentheses as a perfect square:
f(x) = (-(x - 1)^2 - 1)
Therefore, the quadratic function after completing the square is f(x) = -(x - 1)^2 - 1.