Thanks 16 A rectangle is inscribed between the xaxis ndon t

16. A rectangle is inscribed between the x-axis ndon t th parabola ys showa with one side along the x-axis, as shown. 2 6 (xi y a) Write the equation for the area of the rectangle as a function of x. 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? 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). 1.3 Combining Transformation

Solution

(b) since the original equation is

y=9-x^2

And stretch is by factor 4 so the equation given by you is right

y=-(x/4)^2 +9=-x^2 /16+9=9- x^2 /16

The given answer and your answer is same.

(c) for the point (2,5)

Verify equation

y=9-x^2 =9-4=5

For equation y=9-x^2 /16

When x=2

y=9- 4/16=9- 1/4=8.25