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

Answer:

5 seconds

Step-by-step explanation:

ttm/imagine math

Answer 2

Answer:

$t=5\ sec$

Step-by-step 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

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

$t=\frac{-4(+/-)\sqrt{36}} {-2}$

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

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

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

therefore

the solution is $t=5\ sec$