complete the square to rewrite y=x^2-6x+16 in vertex form. Then state weather the vertex is a minimum and give its coordinates

y = (x - 3) ² + 7 is a minimum vertex at (3, 7)

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a (x - h) ² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form using completing the square

• add / subtract (half the coefficient of the x-term) ² to x² - 6x

y = x² + 2 ( - 3) x + 9 - 9 + 16 = (x - 3) ² + 7 ← in vertex form

with vertex = (3, 7)

Since coefficient of x² term > 0 then minimum

minimum vertex at (3, 7)