We can plug in each of the given values to find a, b, and c.
When x = 0, the ax^2 and bx term are 0, so c must be 0.
When x = 1, we have the equation a + b = 2, (no c because it is 0).
Finally, when x = 2, we have the equation 4a + 2b = 5.
Simple system of equations, and in the end we get a = 0.5 and b = 1.5. So the final equation is,
\(0.5x^2+1.5x\)
Plugging in 3,
\(f(3) = 0.5\cdot 9 + 1.5 \cdot 3 \\ f(3) = 4.5 + 4.5 \\ f(3) = 9\)
So our final answer is 9.
\(\)
.
