Maths 多題 - Ans.fyi 參考答案

Maths 多題

hoichung

2006-12-25 2:39 am

1)Find the quotients and the remainders of the following divisions.
1) (9h^3+17h-31)/(9h+3)

2)If f(x) is transformed to g(x),describe the effect of the
transformation on yhe graph of y=f(x).
1) f(x)=x(x+2),g(x)=x^2+4x+3
2) f(x)=2x^2-1,g(x)=2x^2-12x+17

3)Given that the vertex of the graph of the quardratic
y=-8x^2+bx+c is (1/2,1/4),find the a and b.

4)The graph of y=6x^2+5x+q does not interest the x-axis.
Find the range of possible values of q.

回答 (1)

toyszchun

2006-12-29 3:13 am

✔ 最佳答案

1)

9h³+17h-31 = (9h + 3)(h² -1/3 h +2) - 37

∴quotient = h² -1/3 h +2 , remainder = -37

2) 1)

g( x )
=x²+4x+3
=(x+1)(x+3)
=(x+1)[(x+1) + 2]

∴向左移一格

2)

g( x )
= 2x² - 12x + 17

= 2(x - 3)² -1

∴向右移三格

3)find the b and c 嗎???

y= -8x²+bx+c

= -8{x - [-b/2(-8)]} + c - [b²/4(-8)]

=-8(x - b/16)² + c + b²/32

∴b/16 = 1/2

b = 8

c + b²/32 = 1/4

c + 64/32 = 1/4

c = -7/4

4)

因為 does not interest the x-axis

∴Δ ＜ 0

5² - 4(6)(q) ＜ 0

24q ＞ 25

q＞ 25/24

5)

[f(2)]² - [f(-1)]³

=[5(2)(2-3)]² - [5(-1)(-1-3)]³

=100 - 8000

= -7,900

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