Final answer:
The y-value of the maximum/minimum of the function F(x) = x^2 + 12x + 48 is 12.
Step-by-step explanation:
The y-value of the maximum/minimum of the function defined by the equation F(x) = x^2 + 12x + 48 can be found using the vertex formula.
The vertex formula states that the x-value of the maximum/minimum is given by -b/(2a) and the y-value can be found by substituting this x-value back into the function.
In this case, a=1, b=12, and c=48. Plugging these values into the vertex formula, we get the x-value of the maximum/minimum as -12/(2*1) = -6.
Substituting x=-6 back into the function gives us the y-value of the maximum/minimum: F(-6) = (-6)^2 + 12(-6) + 48 = 12.