Question 1166724
i believe your formula needs to be:
A = 50(m-8)^2-3200
the ^ symbol indicates exponentiation.
the * symbol indicates multiplication.
simplify it to get:
A = 50(m^2-16m+64)-3200
simplify further to get:
A = 50m^2 - 800m + 3200 - 3200
simplify further to get:
A = 50m^2 - 800m
set A equal to 0 to get:
0 = 50m^2 - 800m
the equation is now in standard form.
in that form:
a = coefficient of the m^2 term = 50
b is the coefficient of the m term = 800
the max/min point is when m = -b/(2a)]
that becomes m = 800/100 = 8
the quadratic equation is at a minimum/maximum when m = 8
since the coefficient of the m^2 term is positive, than m = 8 is a minimum point in the equation.
if the coefficient of the m^2 term was negative, then m = 8 would be a maximum point in the equation.
note that the normal standard form of a quadratic equation is ax^2 + bx + c = 0.
all that was done here was replace x with m.
the standard form then became am^2 + bm + c = 0.
the min/max equation that is normally x = -b/(2a) became m = -b/(2a).


your min point is when m = 8.
since the formula is A = 50 * (m - 8) ^ 2 - 3200, then the equation becomes -3200 when m = 8 because A = 50 * (8 - 8) ^ 2 - 3200 becomes A = 0 - 3200 which becomes A = -3200.


when m = 18, the formula becomes A = 50 * (18 - 8) ^ 2 - 3200 which becomes A = 50 * 10^2 - 3200 which becomes A = 5000 - 3200 which becomes A = 1800.


this can be shown on the following graph of the equation, where A is represented by y and m is represented by x.


<img src = "http://theo.x10hosting.com/2020/100702.jpg" >