Question 850740
 {{{f(x)=ax^2+bx+5}}}
{{{f'(x)=2ax+b}}}
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{{{f(3)=a(3)^2+b(3)+5=9a+3b+5=2}}}
{{{9a+3b=-3}}}
1.{{{3a+b=-1}}}
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{{{f'(3)=2a(3)+b=2}}}
2.{{{6a+b=2}}}
From eq. 1,
{{{b=-3a-1}}}
Substitute into eq. 2,
{{{6a-3a-1=2}}}
{{{3a=3}}}
{{{a=1}}}
Then,
{{{b=-3(1)-1=-3-1=-4}}}
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{{{f(x)=x^2-4x+5}}}