persamaan kuadrat

no. 1

1a.

titik puncak P(xp,yp) = (0,c) = (0,-16)

melalui (x1,0) = (-4,0) dan (x2,0) = (4,0)

x1 . x2 = c/a

-4 . 4 = -16/a

a = 1

fungsi kuadrat :

f(x) = a(x - x1)(x - x2)

f(x) = a(x - (-4))(x - 4)

f(x) = 1(x + 4)(x - 4)

f(x) = x² - 16

1b.

P(xp,yp) = (2,0)

y = a(x - xp)² + yp

y = a(x - 2)² + 0

melalui (0,8)

8 = a(0 - 2)²

8 = 4a

a = 2

fungsi kuadrat :

f(x) = a(x - xp)² + yp

f(x) = 2(x - 2)²

f(x) = 2(x² - 4x + 4)

f(x) = 2x² - 8x + 8

no. 2

titik balik → titik puncak P(1,-1)

y = a(x - 1)² - 1

melalui (2,3)

3 = a(2 - 1)² - 1

3 = a - 1

a = 4

fungsi kuadrat :

f(x) = a(x - xp)² + yp

f(x) = 4(x - 1)² - 1

f(x) = 4x² - 8x + 3

no. 3

melalui (4,0)

y = ax² + bx + c

0 = a.4² + 4b + c

16a + 4b + c = 0 ... (1)

melalui (1,-3)

a.1² + b.1 + c = -3

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

melalui (-1,3)

a(-1)² + b(-1) + c = 3

a - b + c = 3 ... (3)

persamaan (2) dan (3)

a + b + c = -3

a - b + c = 3

kurangkan

2b = -6

b = -3

persamaan (1) dan (2)

16a + 4b + c = 0

a + b + c = -3

kurangkan

15a + 3b = 3

5a + b = 1

5a - 3 = 1

5a = 4

a = 4/5

persamaan (3)

a - b + c = 3

4/5 - (-3) + c = 3

4/5 + c = 0

c = -4/5

fungsi kuadrat

f(x) = ax² + bx + c

f(x) = 4/5 x² - 3x - 4/5