中四數學題4題～急!!

1a.求a的值

y = ax^2 + 4x - 5

-8 = a(-1)^2 +4(-1) -5
-8 = a - 4 - 5
a = 1
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1b.求頂點的坐標

y = x^2 +4x -5
= x^2 + 4x +2^2 -2^2 - 5
= (x+2)^2 - 4 - 5
= (x+2)^2 - 9

頂點的坐標是 ( -2 , -9 )
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2a.求a、h和k的值

x^2 + 4x = a(x-h)+k
x^2 + 4x +2^2 -2^2 = a(x-h)+k
(x+2)^2 -4 = a(x-h)+k

a的值是 1
h的值是 -2
k的值是 -4
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2b.求次涵數y=x೭+4x的極大值or極小值和對應的x值

y=x^2 + 4x
=( x - 2 ) - 4

極小值是 -4
對應的X值是 x = 2
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3a.求a、t和s的值

2x^2 + 8x = a(x-t)೭+s
2(x^2 + 4x +2^2) - 2(2^2) = a(x-t)೭+s
2( x + 2 )^2 - 8 = a(x-t)೭+s

a的值是 2
t的值是 -2
s的值是 -8
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3b.若涵數y=2x೭+8x+k的極小值是零，求k的值

從(a)
y = 2( x + 2 )^2 - 8 + k

因為極小值是零，所以 ( -8 + k ) = 0。
- 8 + k = 0
k = 8
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4a.求

P = -4x^2 + 2000x -8000
= -4(x^2 - 500x +250^2) - 4(250^2) - 8000
= -4(x - 250 ) ^2 - 258000

每月利潤達至最高時的x值 x = 250

4b.每月最高的利潤 是 258000元。
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258000元