Answer:
vertex is (6, -11)
Explanation:
Given equation
f(x) = x² - 12x + 25
is that of an upward-facing parabola(since the coefficient of x² is positive).
The vertex will be at a minimum and its x-coordinate can be found by finding the first derivative of f(x), setting it equal to zero and solving for x
f'(x) = d/dx(x² - 12x + 25)
= 2x - 12
f'(x) = 0 ==> 2x - 12 = 0
2x = 12
x = 6
Substitute x = 6 in f(x) to get
f(6) = 6² - 12(6) + 25
= 36 - 72 + 25
= -11
So the vertex is at (6, -11)