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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 (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 (minus 2 comma 0) and (6 comma 0). What is the value of c?

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Right! (Applause.)


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 y = (x^2) minus (4 times x) + c) 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 1, 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.

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