SOLUTION: hi i need help with the following Given f(x)=ax^2+b and f(2)=5, f(3)=20, find a and b any help you can provide will be great

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Question 982450: hi i need help with the following
Given f(x)=ax^2+b and f(2)=5, f(3)=20, find a and b
any help you can provide will be great
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First focus on f(2) = 5


f%28x%29=ax%5E2%2Bb


f%282%29=a%282%29%5E2%2Bb Plug in x = 2


f%282%29=4a%2Bb


5=4a%2Bb Replace f(2) with 5


5-4a=b


b=5-4a


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Now move onto f(3) = 20


f%28x%29=ax%5E2%2Bb


f%283%29=a%283%29%5E2%2Bb Replace every x with 3


f%283%29=9a%2Bb


20=9a%2Bb Replace f(3) with 20


20=9a%2B5-4a Replace b with 5-4a


I'll let you finish up. The goal is to isolate 'a'. Once you know the value of 'a', you plug it into b=5-4a to find the value of 'b'.