Answer:
[tex]f(x) = -2x^2 + 7x + 9[/tex]
Step-by-step explanation:
[tex]f(x) = ax^2 + bx + c\\f(0) = 9 => c = 9;\\f(2) = 15 = 4a + 2b + 9 <=> 2a + b = 3\\f(3) = 9a + 3b + 9 = 12 <=> 3a + b = 1\\Subtract the second equation from the first:\\-a = 2 => a = -2; b = 7; c = 9\\f(x) = -2x^2 + 7x + 9[/tex]
