Question

Complete the square to write the function in the form f(x) = a(x - h)² + k.

f(x) = x² - 2x + 5
A: f(x) = (x - 1)² - 4
B: f(x) = (x - (-1))² + 4
C: f(x) = (x - 1)² + 4
D: f(x) = (x - (-4))² - 1

Answer 1

To complete the square for the function f(x) = x² - 2x + 5, we add and subtract (1/2 * -2)² inside the equation to get (x - 1)² + 4, corresponding to option C.

Step-by-step explanation:

To complete the square and write the function f(x) = x² - 2x + 5 in the form f(x) = a(x - h)² + k, we follow these steps:

1. Start with the original equation: f(x) = x² - 2x + 5.
2. Identify the coefficient of the x term, which is -2, and halve it to get -1.
3. Square the result of step 2, yielding 1, and add and subtract this number inside the parentheses: f(x) = (x² - 2x + 1) - 1 + 5.
4. Rewrite the equation with the completed square and combine the constants outside the parentheses: f(x) = (x - 1)² + 4.

The correct form is then f(x) = (x - 1)² + 4, which corresponds to option C.