To rewrite the quadratic function in vertex form y = x² - x + 1, we can complete the square by adding and subtracting the appropriate constants. The quadratic function in vertex form is y = (x - 1/2)² + 3/4.
Step-by-step explanation:
To rewrite the quadratic function in vertex form, we can complete the square. The given quadratic function is y = x² - x + 1. To complete the square, we need to add and subtract a constant from the expression, such that we can write it as a perfect square trinomial.
Starting with y = x² - x + 1, we can rewrite the expression as y = (x² - x + ____ ) + _____ - _____, where the blanks represent the constants we need to add and subtract.
Now, let's complete the square by adding and subtracting the appropriate constants. We have y = (x² - x + 1/4) + _____ - _____.
The first blank can be filled with (1/2)², and the second blank can be filled with 1/4. This gives us y = (x - 1/2)² - 1/4 + 1. Simplifying further, we get y = (x - 1/2)² + 3/4. Therefore, the quadratic function in vertex form is y = (x - 1/2)² + 3/4.