Diketahui sebuah parabola yang melalui titik (0,-4), (-2, 0). dan (-1,-4). Parabola ini

parabola_1

(-1, -4) dan (0,-4)

sumbu simetri = (x1 + x2)/2

xp = (-1 + 0)/2

xp = -1/2

y = (x – xp)² + yp

melalui (-2,0)

0 = (-2 + 1/2)² + yp

yp = -(-3/2)²

yp = -9/4

y1 = (x + 1/2)² – 9/4

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parabola_2

puncak = (xp,yp) = (1,0)

y = a(x – 1)² + 0

melalui (0,1)

1 = a(0 – 1)²

a = 1

y2 = (x – 1)²

titik potong kedua parabola

y1 = y2

(x + 1/2)² – 9/4 = (x – 1)²

(x + 1/2 + x – 1)(x + 1/2 – (x – 1)) = 9/4

(2x – 1/2)(3/2) = 9/4

2x – 1/2 = 9/4 × 2/3

2x = 1/2 + 3/2

2x = 2

x = 1

y = (x – 1)²

y = (1 – 1)²

y = 0

titik potong = (1,0)