每日一题

Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

y = (-2x^2) + (bx) + 5

In the xy-plane, the graph of the equation above assumes its maximum value at x = 2. What is the value of b?

(A)-8
(B)-4
(C) 4
(D) 8
(E) 10

答案和解析

答案：D

解析：

Choice (D) is correct. Since the graph of the quadratic equation y = (-2x^2) + (bx) + 5 assumes its maximum at x = 2, it can be written in the form y = (-2 ((x-2)^2) + k, where k is some constant. This representation is equivalent to y = (-2x^2) + (8x)-8 + k, from which it follows that b = 8 (and-8 + k = 5).