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:

(i) Find the zeroes of the polynomial p(x) from the graph. 

(ii) Find the value of x at which water attains maximum height.

(iii) (A) 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 

(B) 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

(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)