Multiple choice

If a quadratic equation attains its minimum value of - 1 at x = - 2 and of 0 at x = - 1, what is its value at x = - 3?

  1. 0

  2. 1

  3. 2

  4. 3
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A Correct answer
Explanation

A quadratic f(x) = ax^2 + bx + c. Minimum at x=-2 is -1. So f(x) = a(x+2)^2 - 1. We are given f(-1) = 0. a(-1+2)^2 - 1 = 0 => a - 1 = 0 => a = 1. So f(x) = (x+2)^2 - 1. f(-3) = (-3+2)^2 - 1 = (-1)^2 - 1 = 1 - 1 = 0.

AI explanation

Let the quadratic function be f(x) = a(x + 2)2 - 1 based on its vertex form, since it attains its minimum of -1 at x = -2. Using the point that f(-1) = 0, we substitute to get a(-1 + 2)2 - 1 = 0, which gives a = 1. The function is then f(x) = (x + 2)2 - 1. Evaluating at x = -3, we calculate f(-3) = (-3 + 2)2 - 1 = 1 - 1 = 0. The result is 0.

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