Mathematics > Standard Multiple Choice

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

y = (negative 2 times x^2) + (b times x) + 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) negative 8

(B) negative 4

(C) 4

(D) 8

(E) 10 

正确答案>>>

The correct answer is D

Explanation

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