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Given the following three points, find by hand the quadratic function they represent.

(-1, -8), (0, -1), (1, 2)

A. (f(x) = -3x² + 4x - 1)
B. (f(x) = -3x² + 5x - 1)
C. (f(x) = -2x² + 4x - 1)
D. (f(x) = -2x² + 5x - 1)

1 Answer

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Final answer:

The quadratic function represented by the points (-1, -8), (0, -1), and (1, 2) is found by plugging each point into the general quadratic equation and solving for the coefficients, yielding the function f(x) = -2x^2 + 5x - 1.

Step-by-step explanation:

To find the quadratic function that is represented by the points (-1, -8), (0, -1), and (1, 2), we need to solve for the coefficients a, b, and c in the general quadratic equation f(x) = ax^2 + bx + c. We'll plug each point into this equation to create a system of equations:

  • Using (-1, -8): a(-1)^2 + b(-1) + c = -8
  • Using (0, -1): a(0)^2 + b(0) + c = -1
  • Using (1, 2): a(1)^2 + b(1) + c = 2

This simplifies to:

  • a - b + c = -8
  • c = -1
  • a + b + c = 2

We already know that c = -1 from the second equation. Substituting this value into the other equations and solving for a and b, we obtain:

  • a - b - 1 = -8
  • a + b - 1 = 2

Adding those two equations gives us 2a - 2 = -6, so a = -2. Substituting a back into one of the previous equations yields b = 5. Therefore, the quadratic function is f(x) = -2x^2 + 5x - 1, corresponding to option D.

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