For each of the following quadratic functions, find
(a) the optimum value,
(b)(i) the direction of opening,
(ii) the vertex,
(iii) the axis of symmetry
of its graph by completing the square.
1. y=(x+2)(x-3)
2. y=2(2-x)(x+2)-4x
Form 4 maths....好難呀>_<”高手請進....40分
2008-10-15 1:29 am
回答 (1)
2008-10-15 1:58 am
✔ 最佳答案
1. y = x^2 - x -6= (x -1/2)^2 - 1/4 - 6
= (x - 1/2)^2 - 25/4.
Min value = -25/4, opening upwards, vertex is (1/2, -25/4), axis of symmetry is x = 1/2.
2.
y = 4x +8 - 2x^2 -4x - 4x
= -2x^2 - 4x + 8
= -2(x^2 + 2x) + 8
= -2[(x +1)^2 - 1] + 8
= -2(x+1)^2 + 2 + 8
= -2(x +1)^2 + 10
Max value = 10, opening downwards, vertex is (-1, 10), axis of symmetry is
x = -1.
收錄日期: 2021-04-25 22:37:54
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