Question

1) WET SURPRISE A water balloon is launched off of a patio. The path of the water

Answer 1

The function of the water balloon is an illustration of a quadratic function.

The balloon will splat on the ground after 2.5 seconds

The function is given as:

$h(t) = -6t^2 + 13t + 5$

When the balloon splats on the ground, the value of h(t) is 0.

So, we have:

$-6t^2 + 13t + 5 = 0$

Expand the expression

$-6t^2 + 15t- 2t + 5 = 0$

Factorize the above expression

$-3t(2t - 5)- 1(2t - 5 )= 0$

Factor out 2t - 5 in the 2t - 5

$(-3t - 1)(2t - 5 )= 0$

Split the equation into 2

$-3t - 1 = 0\ or\ 2t - 5= 0$

Rewrite as:

$-3t = 1\ or\ 2t = 5$

Solve for t

$t = -\frac 13\ or\ t = \frac 52$

The value of t cannot be less than 0 i.e. negative.

So, we have

$t = \frac 52$

Divide 5 by 2

$t = 2.5$

Hence, the balloon will splat on the ground after 2.5 seconds

Read more about quadratic functions at:

brainly.com/question/11631534