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匿名 發問於 科學及數學數學 · 7 年前

Maths!!!!!

What happen to graph of y = ax^2 + bx + c as

(a) a changes while b and c remain fixed?

(b)b changes (a and c is fixed, a is not equal to 0)?

(c) c changes ( a and b is fixed, a is not equal to 0)?

Give reasons to support your answers?

2 個解答

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  • 7 年前
    最愛解答

    y=ax²+bx+c

    a : determine the concavity of the curve

    b is the slope at the point (0,c)

    c=the y-intercept, ie. point (0, c)

    (c) a, b fixed, a=/= 0

    the y-intercept can be changeable.

    圖片參考:http://imgcld.yimg.com/8/n/HA06881079/o/2013100115...

    (b) a, c fixed, a =/= 0

    the slope at (0, c) can be different.

    圖片參考:http://imgcld.yimg.com/8/n/HA06881079/o/2013100115...

    (a) b, c remain fixed, then the y-intercept and the corresponded slope is fixed, while the concavity can be variant.

    圖片參考:http://imgcld.yimg.com/8/n/HA06881079/o/2013100115...

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  • 7 年前

    c 可以解釋為vertical displacement,但 a, b 要聯合一起看才可以確切指出意思。

    你試把 quadratic function寫成以下的form:

    f(x) = a(x-h)² + k

    其實 h 和 k 都involve a,所以不是單單可以講出 b, c fixed, a change的意思。

    當然,如果roughly都ok的話,那麼 a 可以代表 open upwards 或 open downwards 的程度,如開闊一點或開窄一點。 with fixed x-intercepts

    2013-09-21 15:37:56 補充:

    fix a, c, 問 b changes 就更難說出關係,你可以想像成 fixed y-intercepts 然後放大縮小。

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