persamaan kuadrat

no 1 dan 2 cara sama

no. 2

y = ax² + bx + c

melalui (1,0)

a.1² + b.1 + c = 0

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

melalui (2,11)

a.2² + b.2 + c = 11

4a + 2b + c = 11 ... (2)

pers (1) dan (2)

4a + 2b + c = 11

a + b + c = 0___-

3a + b = 11 ... (3)

melalui (-2,3)

a(-2)² + b(-2) + c = 3

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

pers (2) dan (4)

4a + 2b + c = 11

4a - 2b + c = 3__-

4b = 14

b = 14/4

b = 7/2

3a + b = 11

3a = 11 - b

3a = 11 - 7/2

3a = (22 - 7)/2

a = 15/(2 . 3)

a = 5/2

a + b + c = 0

5/2 + 7/2 + c = 0

6 + c = 0

c = -6

persamaan parabola :

y = 5/2 x² + 7/2 x - 6

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no 3 dan 4 cara sama

no. 3

melalui (1,0) dan (5,0)

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

y = a(x - 1)(x - 5)

melalui (-1,12)

12 = a(-1 -1)(-1 - 5)

12 = a(-2)(-6)

12 = 12a

a = 1

persamaan parabola :

y = 1(x - 1)(x - 5)

y = x² - 6x + 5

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no. 5

P(xp,yp)

P(-2,-3)

y = a(x - xp)² + yp

y = a(x + 2)² - 3

melalui (-1,-2)

-2 = a(-1 + 2)² - 3

-2 = a - 3

a = 1

persamaan parabola :

y = 1(x + 2)² - 3

y = x² + 4x + 1