10分二次函數 - Ans.fyi 參考答案

10分二次函數

2009-12-15 1:15 am

1求下列各二次函數圖像的x截距和y截距
a) y=2x^2+5x+3

b) y=-x^2+14x-49

2)已知函數y=-x^2-4x+12的圖像的對稱軸是x=-2求該圖像的頂點坐標和函數的極大值

3)使用配方法把2次多項式加上1個常數..使得出1個完全平方
a) x^2+2x b) x^2+4x c) x^2-10x

回答 (1)

用戶9112

2009-12-15 3:34 am

✔ 最佳答案

(1a) y = 2x^2 + 5x + 3
當 x = 0, y = 3
y截距 = 3
當 y = 0, 2x^2 + 5x + 3 = 0
(2x + 3)(x + 1) = 0
x = -1.5 或 x = - 1
x截距 = -1 或 -1.5
(1b) y = -x^2 + 14x - 49
當 x = 0, y = - 49
y截距 = -49
當 y = 0, -x^2 + 14x - 49 = 0
x^2 - 14x + 49 = 0
(x - 7)^2 = 0
x = 7
x截距 = 7
(2) y = -x^2-4x+12對稱軸是x=-2
當x = -2, y = -(-2)^2 - 4(-2) + 12 = 16
頂點坐標 = (-2, 16)
函數的極大值 = 16
(3)(a) x^2 + 2x
= x^2 + 2(x) + 1^2 - 1^2
= (x + 1)^2 - 1
(b) x^2 + 4x
= x^2 + 2(2)x + 2^2 - 2^2
= (x + 2)^2 - 4
(c) x^2 - 10x
= x^2 + 2(-5)x + (-5)^2 - (-5)^2
= (x - 5)^2 - 25

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