Question

Radha, an aspiring landscape designer, is tasked with creating a visually captivating pool design that incorporates a unique arrangement of fountains. The challenge entails arranging the fountains in such a way that when water is thrown upwards, it forms the shape of a parabola. The graph of one such parabola is given below.

The height of each fountain rod above water level is 10 cm. The equation of the downward-facing parabola representing the water fountain is given by p(x) = −x² + 5x − 4.

Based on the above information, answer the following questions:

1. Find the zeroes of the polynomial p(x) from the graph.
2. Find the value of x at which water attains maximum height.
3. 1. If h is the maximum height attained by the water stream from the water level of the pool, then find the value of h.
                                              OR
   2. At what point(s) on x- axis, the height of water above x- axis is 2 m?

Answer 1

i. 1 and 4

ii. x = `5/2`

iii. A. At x = `5/2`, p(x) = 2.25,

Therefore, h = 0.10 + 2.25 = 2.35 m

OR

B. −x² + 5x − 4 = 2

x² − 5x + 6 = 0

(x − 2) (x − 3) = 0

⇒ x = 2 and x = 3

Therefore, the required points are (2, 0) and (3, 0).