Answer:
see explanation
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 use the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² - 6x
y = x² + 2(- 3)x + 9 - 9 + 2 = (x - 3)² - 7 ← in vertex form
with vertex = (3, - 7)
To determine whether maximum or minimum consider the value of a
• If a > 0 then minimum
• If a < 0 then maximum
here a = 1 > 0 ⇒ minimum
Hence (3, - 7) is a minimum
