Jawab:

a = -1, b = 2, c = 4

atau

a = -3, b = 6, c = 10

Penjelasan dengan langkah-langkah:

y = ax^2 + bx + c

nilai maks : y = -(b^2-4ac)/ 4a

x = -b/2a

1 = -b/2a

-b = 2a

b = -2a

a^2 + 4 = -(b^2-4ac)/ 4a

a^2 + 4 = -((-2a)^2 - 4ac)/ 4a

a^2 + 4 = -(4a^2 - 4ac)/4a

a^2 + 4 = -4a (a-c)/4a

a^2 + 4 = -a + c

a^2 + a + 4 - c = 0

=>(3,1) = x=3 y=1

y = ax^2 + bx + c

1 + a.9 + 3b + c

1 = 9a + 3(-2a) + a^2 + a + 4

9a - 6a + a^2 + a + 4 -1 = 0

a^2 + 4a + 3 = 0

(a+1) (a+3) = 0

a = (-1)   a = (-3)

b = -2(-1)

   = 2

b = -2(-3)

  = 6

c = (-1)^2 - 1 + 4 = 1 - 1 + 4  = 4

a = -3 => c = (-3)^2 - 3 + 4 = 9-3+4 = 10

a = -1, b = 2, c = 4

atau

a = -3, b = 6, c = 10