Penjelasan dengan langkah-langkah:

persamaan umum grafik

y = ax² + bx + c

melalui titik (-1, 2)

2 = a(-1)² + b(-1) + c

2 = a - b + c

a - b + c = 2 .......................... (1)

melalui titik (1, 6)

6 = a(1)² + b(1) + c

6 = a + b + c

a + b + c = 6 ........................ (2)

melalui titik (2, 4)

4 = a(2)² + b(2) + c

4 = 4a + 2b + c

4a + 2b + c = 4 ................... (3)

eliminasi (2) dan (1)

a + b + c = 6

a - b + c = 2

------------------ -

0 + 2b + 0 = 4

2b = 4

b = 4/2

b = 2

eliminasi (3) dan (1)

4a + 2b + c = 4

. a - b + c = 2

---------------------- -

3a + 3b + 0 = 2

3a + 3b = 2 ........................ (4)

masukan nilai b = 2

3a + 3(2) = 2

3a + 6 = 2

3a = 2 - 6

3a = -4

a = -4/3

subtitusikan nilai a = -4/3 dan b = 2 ke (1)

a - b + c = 2

-4/3 - 2 + c = 2

c = 2 + 2 + 4/3

c = 6/3 + 6/3 + 4/3

c = 16/3

y = ax² + bx + c

y = -4/3x + 2x + 16/3

y = -4/3x + 6/3x +16/3

y = 1/3 (-4x² + 6x + 16)