Answer:

Step-by-step explanation:
Consider the equation that shows flea's motion is
.
Since the origin is located at the point from where the flea jumped,
So,
passes through (0,0).
That is, (0,0) must satisfy
,


Now, it travels 15 cm horizontally from where it started.
That is,
passes through (15,0).

(Because c=0)
...... (1)
Again, it jumps from the ground to a height of 30 cm,
So, the y-coordinate of vertex of
is 30.
Now, the x-coordinate of vertex of the quadratic function must be half of the distance from its starting point to final point.
That is, x-coordinate of the vertex =
= 7.5,
Thus, vertex = (7.5, 30)
(7.5, 30) must satisfy 
That is, 

...... (2)
Equation (1) - 2 × equation (2),
225a - 112.5a = -60
112.5a = -60

From equation (1),




Substitute the values of a, b and c in the quadratic equation
,

Which is the required quadratic equation.