二次函數填充題 暑假作業不會 幫忙謝謝?

1.
原式=16/[(x+1)^2+4]
當 x= -1 時, 原式有最大值 16/4=4 ....Ans

2.
y = - (x-2)^2 + 3
= - x^2 + 4x - 4 + 3
= -x^2 + 4x - 1
a = 4 , b = -1
ab = -4 .....Ans

3.
y = a(x+2)^2 + 7
= ax^2 + 4ax + 4a +7
a + 4a +4a +7=16
9a+7=16
a = 1
y = (x+2)^2+7
= x^2+4x+11 .....Ans

4.
f(1)=a+b+c= -1 .....(1)
f(3)=9a+3b+c= -7 .....(2)
f(5)=25a+5b+c= -5 .....(3)
(2)-(1)
8a+2b= - 6 -----> 4a+b=-3 .....(4)
(3)-(1)
24a+4b= - 4 -----> 6a+b = -1 .....(5)
(5)-(4)
2a=2 ---> a=1 ---> b= -7 ---> c=5
f(x)=x^2-7x+5 ......Ans
=(x-7/2)^2 + 5 - 49/4
=(x-7/2)^2 - 29/4
Ans: (1)f(x)=x^2-7x+5, (2) -29/4