Final answer:
To rewrite the equation y = x² - 2x + 7 in vertex form, we complete the square.
Step-by-step explanation:
To rewrite the equation y = x² - 2x + 7 in vertex form, we complete the square. The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) represents the coordinates of the vertex.
First, we group the x terms together: y = (x² - 2x) + 7. Then, we complete the square for the x terms: y = (x² - 2x + 1) - 1 + 7. Simplifying, we get: y = (x - 1)² + 6.
Therefore, the equation y = x² - 2x + 7 in vertex form is y = (x - 1)² + 6.