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Mathematics>Standard Multiple Choice

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

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

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

答案和解析

答案：A

解析：

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

Alternatively, since the graph of y = (x^2)-(4x) + c) in the xy-plane contains the points (-2，0) and (6，0), and the coefficient of x^2 is 1, the equation is equivalent to y = (x +2)(x-6), which multiplies out to y = (x^2)-(4x)-12. Therefore, c = -12.