14.
由條件知 ax1^2+c = ax2^2+c
=> x1^2 = x^2
= x1 = -x2 (因x1≠x2)
=>x1+x2 = 0
=>函數(shù)值為 a*0^2+c = c
19.
(1)因拋物線經(jīng)過遠點O,所以其拋物線方程為 y = ax^2+bx
入水點坐標為 (4+1-3,-10),即(2,-10)
又,頂點坐標為(-b/2a,2/3)
代入拋物線方程得
-10 = 4a + 2b =>b = -2a - 5
2/3 = a*b^2/4a^2 + b*(-b/2a) = -b^2/4a
聯(lián)立解二元二次方程組,得
a = -25/6,b = 10/3
a = -3/2 ,b = -2
由圖可知,拋物線對稱軸的x坐標大于0,因此a,b必定異號,
所以a = -25/6,b = 10/3
得拋物線方程：y = -25/6*x^2 + 10/3*x
(2) 運動員在空中調(diào)整好入水姿勢時的x坐標為 (18/5+1-3) = 8/5
代入拋物線方程得
y = -25/6 * 64/25 + 10/3* 8/5 = -16/3 < -5
此時,顯然跳水運動員距水面高度小于5m了,因此跳水會失誤.