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If $f(0)=0$, $f(1)=2$, $f(2)=5$ and $f(x)=ax^2+bx+c$, what is the value of $f(3)$?

 Jul 16, 2021
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f(0) = a*0^2 + b*0 + c = 0

0a + 0b + c = 0

c = 0

f(1) = a*1^2 + b*1 + c = 2

a + b + c = 2

a + b = 2

f(2) = a*2^2 + b*2 + c = 5

4a + 2b + c = 5

4a + 2b = 5

2a = 1

a = .5

b = 1.5

f(x) = .5x^2 + 1.5x + 0

f(3) = .5(3)^2 + 1.5(3) + 0 = 9

 

=^._.^=

 Jul 16, 2021

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