SOLUTION: Given that f(x)=ax^2+bx+5, f(3)=2 and f'(3)=2 find the values of a and b

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Question 850740: Given that f(x)=ax^2+bx+5, f(3)=2 and f'(3)=2 find the values of a and b
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=ax%5E2%2Bbx%2B5
f%27%28x%29=2ax%2Bb
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f%283%29=a%283%29%5E2%2Bb%283%29%2B5=9a%2B3b%2B5=2
9a%2B3b=-3
1.3a%2Bb=-1
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f%27%283%29=2a%283%29%2Bb=2
2.6a%2Bb=2
From eq. 1,
b=-3a-1
Substitute into eq. 2,
6a-3a-1=2
3a=3
a=1
Then,
b=-3%281%29-1=-3-1=-4
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f%28x%29=x%5E2-4x%2B5