Question

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.

Answer 1

Answer:

Area of Rectangle = $26x - 2x^3$

Step-by-step explanation:

Rectangle two vertices lie on x axis ; two vertices lie on parabola $y = 13 - x^2$.

Supposing coordinates of upper right vertex of rectangle are P = $x , y$

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

Width of rectangle = $2x$

Length of rectangle = $y$  ; $y = 13 - x^2$

Area of Rectangle = Length x Width

= $2x (y)$

= $2x (13 - x^2)$

= $26x - 2x^3$