Find a such that f(x)=ax²-4x+3 has a maximum value of 12

a = -4/9

Step-by-step explanation:

For a function y = ax² + bx + c, the maximum value is at x = -b/(2a).

f(x) = ax² − 4x + 3

Here, the maximum value is at x = -(-4)/(2a) = 2/a.  Setting f(x) = 12 at this point:

12 = a (2/a)² − 4 (2/a) + 3

12 = 4/a − 8/a + 3

9 = -4/a

a = -4/9

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm