Math: Advanced Math

SAT Question of the Day for October 18, 2026

The function h(x)=−2(x−4)2+13h(x) = -2(x - 4)^2 + 13 has a maximum value. What is this maximum value, and at what value of xx does it occur?
  1. A.Maximum value of 44 at x=13x = 13
  2. B.Maximum value of 1313 at x=−4x = -4
  3. C.Maximum value of −13-13 at x=4x = 4
  4. D.Maximum value of 1313 at x=4x = 4Correct answer

Explanation

The function h(x)=−2(x−4)2+13h(x) = -2(x - 4)^2 + 13 is in vertex form a(x−h)2+ka(x - h)^2 + k with a=−2a = -2, h=4h = 4, and k=13k = 13. Since a<0a < 0, the parabola opens downward and the vertex (4,13)(4, 13) is the maximum point. The maximum value is 1313 at x=4x = 4. The distractor stating x=−4x = -4 confuses the sign of hh in the vertex form (x−h)(x - h). The distractor stating a maximum of −13-13 incorrectly negates kk. The distractor swapping the values 44 and 1313 reflects confusion between the vertex coordinates and their roles as the xx-value and maximum output.

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