Completing the square transforms x^2 - 3x = -1 into the more revealing form (x - 3/2)^2 = 5/4. This representation facilitates the identification of key features, such as the vertex (h, k).
To complete the square for the quadratic equation x^2 - 3x = -1, we aim to rewrite it in the form (x - h)^2 = k, where h and k are constants.
Starting with the given equation, x^2 - 3x = -1, we add and subtract (3/2)^2 inside the parentheses to complete the square. This is because (a/2)^2 is the square needed to complete the square for ax. In this case, a = -3, so (3/2)^2 = 9/4.
Adding and subtracting 9/4, the equation becomes (x^2 - 3x + 9/4) - 9/4 = -1.
Simplifying, we have (x - 3/2)^2 = 5/4. Therefore, the equation in completed square form is (x - 3/2)^2 = 5/4. This form makes it easier to identify key features of the quadratic function, such as the vertex (h, k), where h = 3/2 and k = 5/4.