在
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
解释：
Use the fact that y = (-2x^2) + bx + 5 assumes its maximum value at x = 2 to write this quadratic equation in the form y = a times ((x - h)^2) + k.
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 = -2 x^2 + 8x - 8 + k, from which it follows that b = 8 (and -8 + k = 5).
y = -2x^2 + (bx) + 5
=-2[(x-b/4)^2+(b^2)/16-5]
这是开口向下的二次函数，在x=2时达到最大值，所以x-b/4=0，从而得出b=8.
正确答案是D。
A geologist has 10 rocks of equal weight. If 6 rocks and a 10-ounce weight balance on a scale with 4 rocks and a 22-ounce weight, what is the weight, in ounces, of one of these rocks?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
解释：
If r is the weight of one rock, then the weight of 6 rocks and a 10-ounce weight can be written as (6 times r) + 10, and the weight of 4 rocks and a 22-ounce weight can be written as (4 times r) plus 22. Since the two sides balance, these weights are equal.Since the two weights balance, you can write the equation (6 times r) +10 = (4 times r) + 22. Solving this equation yields r equals 6.
正确答案是C
相关推荐: