Multiple choice

x f(x) -1 18 0 24 1 32 For the quadratic function f, the table shows three values of x and their corresponding values of f(x). Which equation defines f?

  1. f(x) = 3x2 + 5x + 24

  2. f(x) = x2 + 7x + 24

  3. f(x) = 5x2 – x + 24

  4. f(x) = 9x2 + x + 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Substitute the given x-values into the options to check for consistency. For x=0, all options yield f(0)=24, which matches the table. For x=1, f(1) must be 32; option B gives 1^2 + 7(1) + 24 = 32, which is correct.

AI explanation

Assume the quadratic function is f(x) = Ax^2 + Bx + C. Using the given table values, we set up the equations A(0)^2 + B(0) + C = 24, A(1)^2 + B(1) + C = 32, and A(-1)^2 + B(-1) + C = 18. Solving this system yields C = 24, A + B = 8, and A - B = -6. Solving for A and B gives A = 1 and B = 7, so the defining equation is f(x) = x^2 + 7x + 24.

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