When a stone is thrown upward, it follows a parabolic path given by a form of the equation . If represents ground level, find the equation of a stone that is thrown from ground level at and lands on the ground 130 units away if the stone reaches a maximum height of 130 units.

Question

When a stone is thrown upward, it follows a parabolic path given by a form of the equation  . If  represents ground level, find the equation of a stone that is thrown from ground level at  and lands on the ground 130 units away if the stone reaches a maximum height of 130 units. ​

Quizplus · Accepted Answer

Let the stone's equation be y = a(x-p)^2 + q. 
Since the stone starts at ground level, q = 0. 
And since it reaches a maximum height of 130 units, a = -1/130(130)^2 = -130. 
So the equation of the stone is y = -130(x-p)^2. 
To find p, we know that the stone lands 130 units away, so p = 65. 
Therefore, the equation of the stone is y = -130(x-65)^2 which matches option B.

When a Stone Is Thrown Upward, It Follows a Parabolic