Question

Tentukan persamaan fungsi kuadrat yang mempunyai titik puncak (-2,0) dan melalui titik (0,1)

Answer 1

Bentuk fungsi kuadrat :

f(x) = ax² + bx + c

xpuncak = -b/2a
-2 = -b/2a
-4a = -b
b = 4a

f(x) = ax² + 4ax + c

f(0) = 1
a(0)² + 4a(0) + c = 1
c = 1

f (x) = ax² + 4ax + 1
f (-2) = 0
a(-2)² + 4a(-2) + 1 = 0
4a - 8a + 1 = 0
-4a + 1 = 0
4a - 1 = 0
4a = 1
a = 1/4

f (x) = 1/4x² + 4(1/4)x + 1
f (x) = 1/4x² + x + 1

y = 1/4x² + x + 1

Answer 2

f(x) = ax² + bx + c

x puncak = -b/2a
-2 = -b/2a
-4a = -b
b = 4a

f(x) = ax² + 4ax + c

f(0) = 1
a(0)² + 4a(0) + c = 1
c = 1

f (x) = ax² + 4ax + 1
f (-2) = 0
a(-2)² + 4a(-2) + 1 = 0
4a - 8a + 1 = 0
-4a + 1 = 0
4a - 1 = 0
4a = 1
a = 1/4

f (x) = 1/4x² + 4(1/4)x + 1
f (x) = 1/4x² + x + 1

y = 1/4x² + x + 1