Question

Tentukan fungsi kuadrat yang melalui
titik (4,5) dan titik puncanya (-2,1)

Answer 1

tentukan fungsi kuadrat yang melalui 
titik (4,5) dan titik puncanya (-2,1)
y-Yp = k (x - Xp) ²
y-1 = k (x + 2)²
5-1 = k (4+2)²
4 = 36k
k = 4/36 = 1/9

y-1 = 1/9 (x+2)²
y-1 = 1/9 (x² + 4x + 4)
y = 1/9x² + 4/9x +4/9 +1
y = 1/9x² + 4/9x + 13/9 atau y = 1/9(x² + 4x +13)

Answer 2

Misal y = ax^2 + bx + c melalui (4,5) 5 = 16a + 4b + c .................. (1) titik puncak (-2,1) x puncak = -b/2a -2 = -b/2a b = 4a ................... (2) y puncak = (-b^2+4ac)/4a 1 = (-b^2+4ac)/4a 4a = -b^2+4ac ............ (3) substitusi pers (2) ke (3) 4a = -(4a)^2 + 4ac 4a = -16a^2 + 4ac 1 = -4a + c ...................(4) substitusi pers (2) ke (1) 5 = 16a + 16a + c 5 = 32a + c ............... (5) eliminasi c dari pers (4) dan (5), didapat 36a = 4 a = 1/9 b = 4a = 4/9 -4a + c = 1 -4/9 + c = 1 c = 13/9 maka y = 1/9 x^2 + 4/9 x + 13/9 atau y = 1/9(x^2 +4x+13)