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　　The graph of y = (2x - 4)(x - 4) is a parabola in the xy-plane. In which of the following equivalent equations do the x- and y-coordinates of the vertex of the parabola appear as constants or coefficients?

　　Content: Passport to Advanced Math

　　Key: C

　　Objective: You must be able to see structure in expressions and equations

　　and create a new form of an expression that reveals a specific property.

　　Explanation: Choice C is correct. The equation y = (2x - 4)(x - 4) can be written

　　in vertex form, y = a + k, to display the vertex, (h, k), of the parabola. To put

　　the equation in vertex form, first multiply: (2x - 4)(x -4) = 2 -8x-4x+16.

　　Then, add like terms, - 8x - 4x +16 = - 12x + 16. The next step is com-

　　pleting the square.

　　Therefore, the coordinates of the vertex, (3, -2), are only both revealed in

　　choice C. Since you are told that all of the equations are equivalent, simply

　　knowing the form that displays the coordinates of the vertex will save all of

　　these steps — this is known as "seeing structure in the expression or equation."

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