Jawab:
[Soal nomor 2]     f(x) = -2x² + 2x + 5  ✅
[Soal di gambar]  f(x) = (x²/2) - (x/2) - 10  ✅

Penjelasan:
(2)  Diketahui fungsi f(x)
Melalui titik (1, 5), (2, 1), (-2, -7)

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

Untuk koordinat (1, 5) dimana x = 1, f(x) = 5
f(x) = ax² + bx + c
5 = a(1²) + b(1) + c
5 = a + b + c   [pers i]

Untuk koordinat (2, 1) dimana x = 2, f(x) = 1
f(x) = ax² + bx + c
1 = a(2²) + b(2) + c
1 = 4a + 2b + c   [pers ii]

Untuk koordinat (-2, -7) dimana x = -2, f(x) = -7
f(x) = ax² + bx + c
-7 = a((-2)²) + b(-2) + c
-7 = 4a - 2b + c   [pers iii]

Eliminasi pers ii dengan pers iii
1 = 4a + 2b + c   [pers ii]
-7 = 4a - 2b + c   [pers iii]
---------------------- +
-6 = 8a  + 2c
-6 = 2(4a+c)
-6/2 = 4a+c
-3 = 4a + c   [pers iv]

Eliminasi pers iv dengan pers ii
-3 = 4a    + c   [pers iv]
1 = 4a + 2b + c   [pers ii]
-------------------- (-)
-4 =      -2b
b = -4/-2
b = 2

Substitusi b dengan 2
5 = a + b + c   [pers i]
5 = a + 2 + c
5-2 = a + c
3 = a + c [pers v]

Eliminasi pers v dengan pers iv
3 = a    + c [pers v]
-3 = 4a + c   [pers iv]
--------------- (-)
6 = -3a
a = 6/(-3)
a = -2

Substitusi b dengan 2
dan a dengan -2
5 = a + b + c   [pers i]
5 = -2 + 2 + c
c = 5

Rumus fungsi kuadrat
f(x) = ax² + bx + c
f(x) = -2x² + 2x + 5  ✅

————————————

[soal di gambar]
Diketahui fungsi kuadrat f(x)
melewati (-4, 0), (5, 0), dan (2, -9)

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

Untuk koordinat (-4, 0) dimana x = -4, f(x) = 0
f(x) = ax² + bx + c
0 = a((-4)²) + b(-4) + c
0 = 16a - 4b + c   [pers i]

Untuk koordinat (5, 0) dimana x = 5, f(x) = 0
f(x) = ax² + bx + c
0 = a(5²) + b(5) + c
0 = 25a + 5b + c   [pers ii]

Untuk koordinat (2, -9) dimana x = 2, f(x) = -9
f(x) = ax² + bx + c
-9 = a(2²) + b(2) + c
-9 = 4a + 2b + c   [pers iii]

Substitusi pers i dengan pers ii
16a - 4b + c  =  25a + 5b + c
16a - 4b  =  25a + 5b
25a - 16a = -5b - 4b
9a = -9b
a = -b  [pers iv]

Substitusi nilai a = -b
-9 = 4a + 2b + c   [pers iii]
-9 = 4(-b)+2b+c
-9 = -4b+2b+c
-9 = -2b + c  [pers iv]

0 = 16a - 4b + c
0 = 16(-b) - 4b + c
0 = -16b-4b + c
0 = -20b + c  [pers v]

Eliminasi pers iv dengan pers v
-9 = -2b + c
0 = -20b + c
------------------ -
-9 = 18b
b = -9/18
b = -½

a = -b  [pers iv]
a = -(-½)
a = ½

0 = 16a - 4b + c   [pers i]
0 = 16(½) - 4(-½) + c
0 = 8 - (-2) + c
0 = 10 + c
c = -10

Rumus fungsi kuadrat
f(x) = ax² + bx + c
f(x) = ½ x² - ½x- 10
atau
f(x) = (x²/2) - (x/2) - 10  ✅

——————————————
(xcvi)