Question

This activity will help you meet these educational goals:

Answer 1

Answer:

A

$h = -16t^2 + 192t$

B

Vertex=(6,576)

Step-by-step explanation:

The problem gives us the following data:

$v_o=192\ ft/s,\ h_o=0$

A.

Thus the function is

$h = -16t^2 + 192t$

The graph of h has the shape of an inverted parabola. Recall if the coefficient of the quadratic term is negative, the parabola is concave down, so it has a maximum value.

Part B

Let's take the function of h

$h = -16t^2 + 192t$

Factoring by -16

$\displaystyle h = -16(t^2 - 12t)$

Completing squares

$\displaystyle h = -16(t^2 - 12t+36-36)$

$\displaystyle h = -16(t^2 - 12t+36)+576$

Factoring

$\displaystyle h = -16(t-6)^2+576$

Rearranging

$\displaystyle h -576= -16(t-6)^2$

We can get the coordinates of the vertex from this standard form of the parabola.

Vertex=(6,576)

The maximum value means that at t=6 seconds, the firework will be 576 feet high and then it will start falling back to the ground.