SAT I 一日一问：2013年6月28日-打印版式-

Mathematics > Standard Multiple Choice

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

y = (x^2) minus (4 times x) + c)

In the quadratic equation above, c is a constant. The graph of the equation in the x y plane contains the points (-2,0) and (6,0). What is the value of ?

(A) -12
(B) -6
(C) 4
(D) 6
(E) 12

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The Correct answer is A.

Explanation

Since the graph of y = (x^2) minus (4 times x) + c in the xy-plane contains the point (negative 2 comma 0) , it follows that substituting the value x = negative 2 into yields y = 0 . Hence 0 = ((negative 2)^2) minus 4 times (negative 2) + c , which simplifies to 0 = 4 minus (negative 8) + c , or 0 = 12 + c . Therefore, c = negative 12 .

Alternatively, since the graph of y = (x^2) minus (4 times x) + c) in the xy-plane contains the points (negative 2 comma 0) and (6 comma 0) , and the coefficient of x^2 is , the equation is equivalent to y = (x +2) times (x minus 6) , which multiplies out to y = (x^2) minus (4 times x) minus 12 . Therefore, c = negative12 .