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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 7, 2021

#1
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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.



Jul 7, 2021
#2
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Thank you!

Guest Jul 7, 2021