tentukan persamaan fungsi kuadrat yang melalui titik (4,-7) (1,-16) dan (0,-15)

jawab

misal fungsi kuadrat
f(x) = ax² + bx + c

(4,-7) → a(4²) + b(4) + c = -7
16a + 4b + c = -7...(i)

(1,-16) → a(1²) + b(1) + c = -16
a + b + c = -16...(ii)

(0, -15) →a(0²) + b(0) + c = -15
c = -15...(iii)

c = - 15 sub ke i
16a + 4b  - 15 = -7
16a + 4b = 8
4a + b = 2...(iv)

c = -15 sub k e ii
a+ b - 15 = -16
a + b = -1 .....(v)

(iv) dan (v)
4a + b = 2
a + b = -1 ...| (-)
3a  = 3
a = 3

a + b = - 1
3 + b = - 1
b = - 4

fungsi kuadrat   f(x) = ax² + bx + c
f(x) = 3x² - 4x  - 15