Question

已知二次函数y=f(x)的最大值等于13,且f(3)=f(1)=5,求f(x)解析式

Answer 1

let

f(x)= ax^2+ bx + c

f(3)= 9a+3b+c = 5 --(1)

f(1)= a+ b +c = 5 ---(2)

(1)-(2)

8a+2b=0

b= -4a ---(3)

f'(x)= 2ax+b

f'(x)=0 => x=-b/2a

f(-b/2a)= f(2)

= 4a+2b+c = 13 ---_(4)

(1)- (4)

5a+b= -8

5a-4a=-8

a = -8

b = 32

c = -19

f(x)= -8x^2+32x-19 #