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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) - (4 times x) +c

In the quadratic equation above, 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 ?

Correct!

Explanation

The correct answer is (A). Since the graph of y = (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 = (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 .