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

Answer 1

let's complete the square
f(x) = a[ x^2 -4/a + 4/a^2 - 4/a^2] + 3
= a(x-2/a) -4/a + 3

so -4/a + 3 = 12
-4a = 9
a = -9/4