I need help getting the difference quotient for these 3 ques

I need help getting the difference quotient for these 3 questions! please help!

Find the difference Quotient for f(x): f(x) = 3x^2 - 2x + 8 f(x) = 1/2 x^2 + 3x - 7 f(x) = -5x^2 + 2x -9

Solution

a)given f(x)=3x² -2x+8

f(x+h)=3(x+h)² -2(x+h)+8

f(x+h)=3(x²+2xh+h²) -2x-2h+8

f(x+h)=3x²+6xh+3h² -2x-2h+8

f(x+h)-f(x)=3x²+6xh+3h² -2x-2h+8-3x² +2x-8

f(x+h)-f(x)=6xh+3h² -2h

difference coefficient =[f(x+h)-f(x)]_/h

difference coefficient =[6xh+3h² -2h]_/h

difference coefficient =6x+3h -2

b)given f(x)=(1/2)x² +3x-7

f(x+h)=(1/2)(x+h)² +3(x+h)-7

f(x+h)=(1/2)(x²+2xh+h²) +3x+3h-7

f(x+h)=(1/2)x²+xh+(1/2)h² +3x+3h-7

f(x+h)-f(x)=(1/2)x²+xh+(1/2)h² +3x+3h-7 -(1/2)x² -3x+7

f(x+h)-f(x)=xh+(1/2)h² +3h

difference coefficient =[f(x+h)-f(x)]_/h

difference coefficient =[xh+(1/2)h² +3h]_/h

difference coefficient =x+(1/2)h +3

c)given f(x)=-5x² +2x-9

f(x+h)=-5(x+h)² +2(x+h)-9

f(x+h)=-5(x²+2xh+h²) +2x+2h-9

f(x+h)=-5x²-10xh-5h² +2x+2h-9

f(x+h)-f(x)=-5x²-10xh-5h² +2x+2h-9 -(-5x² +2x-9)

f(x+h)-f(x)=-5x²-10xh-5h² +2x+2h-9 +5x² -2x+9

f(x+h)-f(x)=-10xh-5h² +2h

difference coefficient =[f(x+h)-f(x)]_/h

difference coefficient =[-10xh-5h² +2h]_/h

difference coefficient =-10x-5h +2