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Find the function f(x) = ax^2 + bx + c. If f(1) = 6, f(-3) = 22, f(3) = 10, what is f(x)?

User RafH
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Final answer:

To find the function f(x) = ax^2 + bx + c, we can use the given values of f(1), f(-3), and f(3) to solve for the coefficients a, b, and c.

Step-by-step explanation:

To find the function f(x) = ax^2 + bx + c, we can use the given values of f(1), f(-3), and f(3) to solve for the coefficients a, b, and c.

Substituting x = 1 into the function gives us: 1a + 1b + c = 6. This can be written as a + b + c = 6.

Similarly, substituting x = -3 gives us: 9a - 3b + c = 22, and substituting x = 3 gives us: 9a + 3b + c = 10.

We now have a system of three equations with three variables which can be solved to find the values of a, b, and c.

User Dmcnelis
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