Question: calculus 12 3. (15 marks) A rectangle is inscribed between the x-axis and the parabola y = 9- x? with one side along the x-axis,

calculus 12

3. (15 marks) A rectangle is inscribed between the x-axis and the parabola y = 9- x? with one side along the x-axis, as shown. a. Write the equation for the area of the rectangle as a function of x. (4 marks) b. Suppose a horizontal stretch by a factor of 4 is applied to the parabola. What is the equation for the area of the transformed rectangle? (6 marks) c. Suppose the point (2,5) is the vertex of the rectangle on the original parabola. Use this point to verify your equations from parts a and b. (5 marks) y =9-X 8- (x y ) 4 2. ( x, 0) -4 -2 0 2 4 X

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