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

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)

The answer is