Multiple choice

Find the maximum/minimum value of the quadratic expression $\displaystyle -x^{2}+8x+1$

  1. Minimum value is $17$
  2. Minimum value is $-34$
  3. Maximum value is $17$
  4. Maximum value is $34$
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C Correct answer
Explanation

The expression is -x^2 + 8x + 1. This is a downward-opening parabola. The maximum occurs at x = -b/(2a) = -8/(2*-1) = 4. Max value = -(4)^2 + 8(4) + 1 = -16 + 32 + 1 = 17.

AI explanation

For the quadratic expression -x^2 + 8x + 1, the coefficient of x^2 is negative, indicating that the parabola opens downwards and will have a maximum value. The maximum value of a quadratic ax^2 + bx + c occurs at x = -b/(2a). Substituting the values gives x = -8/(2 * -1) = 4. Plugging x = 4 back into the expression yields -(4)^2 + 8(4) + 1 = -16 + 32 + 1 = 17, confirming the maximum value is 17.

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