Question

高中文科导数f（x）1.已知曲线f(x)=ax^2+bx+c过点p（1,1）,在点q（2,-1）的切线为y=x-3,求a

Answer 1

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

过点p（1,1）

a+b+c= 1 (1)

q（2,-1）

4a+2b+c = -1 (2)

f'(x) = 2ax+b

f'(2) = 2a+b = 1 (3)

(2)-(1)

3a+b= -2 (4)

(4)-(3)

a = -3

from (4)

3(-3)+b=-2

b= 7

from(1)

-3+7+c = 1

c=-3

f(x)=-3x^2+7x-3