#1**0 **

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**.

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Awesomeguy Jul 7, 2021