To identify the vertex, axis of symmetry, and min/max value of the function f(x) = x^2 - 12x + 44, we can use the formula:
Vertex = (-b/2a, f(-b/2a))
Axis of symmetry = -b/2a
Min/max value = f(-b/2a)
From the given function, we can see that a = 1 and b = -12. Plugging these values into the formula, we get:
Axis of symmetry = -b/2a = -(-12)/(2*1) = 6
To find the vertex, we need to evaluate f(6) since the x-coordinate of the vertex is 6.
f(6) = 6^2 - 12(6) + 44 = 4
Therefore, the vertex is (6, 4).
The min/max value of the function is the y-coordinate of the vertex, which is 4. Since the coefficient of the x^2 term is positive, the parabola opens upwards, so the vertex corresponds to the minimum value of the function.
Therefore, the min value of the function is 4.
(If you’re confused or don’t understand please comment so I can help you!)