Question

A water balloon is 5 feet above the ground when Sally launches it into the air. Use the quadratic equation 0 = -t^2 + 4t + 5 to find how much time, t, it takes for the water balloon to reach the ground.

Answer 1

5 seconds

Explanation:

ttm/imagine math

Answer 2

`t=5\ sec`

Explanation:

we have

`-t^(2) +4t+5=0`

Solve the quadratic equation to find the zero's or x-intercepts

Remember that

The x-intercepts are the values of x when the value of y is equal to zero ( water balloon reach the ground)

we know that

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`-t^(2) +4t+5=0`

so

`a=-1\\b=4\\c=5`

substitute in the formula

`t=\frac{-4(+/-)\sqrt{4^(2)-4(-1)(5)}} {2(-1)}`

`t=\frac{-4(+/-)√(36)} {-2}`

`t=\frac{-4(+/-)6} {-2}`

`t=\frac{-4(+)6} {-2}=-1`

`t=\frac{-4(-)6} {-2}=5`

therefore

the solution is
`t=5\ sec`