47. In the standard (x, y) coordinate plane below, 1 side of a rectangle is on the x-axis, and the vertices of the opposite side of the rectangle are on the graph of the parabola y = 6 - 2x2. Let a represent any value of x such that 0 < x < . Which of the following is an expression in terms of a for the area, in square coordinate units, of any such rectangle ?

Answer and Explanation

Your Answer is

Correct Answer is A

Explanation

Ask what the area of ​​the rectangle should be expressed in a. From the figure, it can be seen that the length of the rectangle is 2a, and the width is 6-2a2, so the area is 2a×( 6-2a2 )=-4a3 +12a.