Write the quadratic function in vertex form.

y = x^2 - 6x + 7

The vertex form: y = a (x - h) ² + k

y = x² - 6x + 7 = x² - 2x · 3 + 3² - 3² + 7 = (x - 3) ² - 9 + 7 = (x - 3) ² - 2

Answer: y = (x - 3) ² - 2

Used: (a - b) ² = a² - 2ab + b²

To solve this equation, we can use completing of the squares. Hence, from the equation y = x^2 - 6x + 7, b is equal to - 6. The form should become y = (x - (b/2) ^2) + c. (b/2) ^2 is equal to 9. Hence,

y = (x - 3) ^2 - 9 + 7

y = (x - 3) ^2 - 2

y - 2 = (x - 3) ^2

hence the vertex is at (3,2)