Multiple choice

The values of a quadratic function f(x) is a positive for all values of x, except for x = 4. If f(0) = 10. Find the value of f( −4).

  1. 46

  2. 40

  3. 80

  4. 38
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B Correct answer
Explanation

Since f(x) > 0 for all x except x=4, f(x) must be of the form k(x-4)^2. Given f(0) = 10, k(0-4)^2 = 10 => 16k = 10 => k = 10/16 = 5/8. Then f(-4) = (5/8)(-4-4)^2 = (5/8)(64) = 40.

AI explanation

Since the quadratic function is positive for all x except at x equals 4, the function reaches its minimum value of 0 at x equals 4, meaning its vertex is at 4 and it can be written as f(x) equals a times (x minus 4) squared. Using the given condition f(0) equals 10, we substitute x with 0 to get a times 16 equals 10, so a is 5 over 8. Now, evaluating f(-4) gives 5 over 8 times (-4 minus 4) squared, which is 5 over 8 times 64, resulting in 40.

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