Multiple choice

The table below lists the values of a quadratic function g(x) at three different points: x g(x) -1 10 0 14 1 20 Which equation best represents the function g(x)?

  1. g(x) = 2x2 + 4x + 14

  2. g(x) = x2 + 5x + 14

  3. g(x) = 3x2 - x + 14

  4. g(x) = 4x2 + x + 14
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Test the points: For x=0, g(0)=14. All options satisfy this. For x=1, g(1)=20. Option B: 1^2 + 5(1) + 14 = 20. Correct. For x=-1, g(-1)=(-1)^2 + 5(-1) + 14 = 1 - 5 + 14 = 10. Correct.

AI explanation

Using the vertex form of a quadratic function, we can write g(x) = ax^2 + bx + c. Substituting the point (0, 14) gives c = 14. Using the points (-1, 10) and (1, 20) creates the equations a - b + 14 = 10 and a + b + 14 = 20, which simplify to a - b = -4 and a + b = 6; solving this system yields a = 1 and b = 5, making the equation g(x) = x^2 + 5x + 14.

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