If f(0)=0, f(1)=2, f(2)=5 and f(x)=ax^2+bx+c, what is the value of f(3)?
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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)
If f(0) = 0, then c = 0
So we have these two equations for f(1) and f(2)
a(1)^2 + b(1) = 2 → a + b = 2 (1)
a(2)^2 + b(2) = 5 → 4a + 2b = 5 (2)
Multiply (1) by - 2 → -2a - 2b = -4 add this to (2)
2a = 1 → a = 1/2
And subbing this into (1) to find b
1/2 + b = 2 → b = 3/2
So our function is
f(x) = (1/2)x^2 + (3/2)x
So f(3) = (1/2) (3)^2 + (3/2) (3) = 9/2 + 9/2 = 18/2 = 9