Question

Jake throws a stone off a bridge into the river. The stones height in meters above the water is based on the time in seconds after jake threw the stone. The quadratic equation y=-5^2+10x+15 represents the scenario

Answer 1

The stone will hit the water after 3 seconds

Explanation:

Given

`y = -5x^2 + 10x +15`

Required

At what time will the stone enter the water

When the stone enters the water;

`y = 0`

So, we have:

`-5x^2 + 10x +15 = 0`

Divide through by -5

`x^2 -2x -3 = 0`

Expand

`x^2 +x -3x -3 = 0`

Factorize

`x(x +1) -3(x +1) = 0`

Factor out x + 1

`(x -3) (x +1) = 0`

Solve for x

`x - 3 = 0\ or\ x + 1 = 0`

`x = 3\ or\ x = -1`

x (time) cannot be negative.

So:

`x = 3`