The base of a rectangle lies on the x-axis, while the upper two vertices lie on the parabola y = 13 − x2. Suppose that the coordinates of the upper right vertex of the rectangle are (x, y). Express the area of the rectangle as a function of x.

Area of Rectangle =

Step-by-step explanation:

Rectangle two vertices lie on x axis ; two vertices lie on parabola .

Supposing coordinates of upper right vertex of rectangle are P =

Due to parabola symmetry, width of rectangle is twice the distance  horizontal (X) axis distance between Y axis & point P.

Width of rectangle =

Length of rectangle =  ;

Area of Rectangle = Length x Width

=

=

=

Step-by-step explanation:

x is all real numbers