How do you solve this?

 An object is launched into the air from the top of a building. 

 Its height, in feet, after t seconds is given by h(t) = -16t^2 + 96t + 260 

 Answer the following questions: 

 a. 

 What was the height of the building the object was launched from? 

 b. 

 What is the maximum height the object reaches? 

 c. 

 How long will it take for the object to hit the ground?

y(t) = ½at² + v₀t  + y₀ is the basic formula you need to know.

y₀ is the original height at t=0, in this case that's 260 feet

Max height time is given by t= -b/2a from the Quadratic Formula, or t=96/32 = 3 sec

h(3) = -16*3² +96*3 +260 = 404 feet max height

You have a function the represents the height, in feet, t seconds after the object is launched.

h(t) = -16t² + 96t + 260

PART A:

Since the object is being launched from the top of the building, at time t = 0, the height will be equal to the height of the building (right?).

So just calculate h(0). The first two terms cancel out and you get:

h(0) = 260

PART B:

The function given is an upside-down parabola. It will be at its highest point at the vertex of the parabola. Remember, that if you have a quadratic of the form:

ax² + bx + c, then the x-coordinate of the vertex is found using:

x = -b/(2a)

If you have trouble remembering this, just think about the full quadratic formula. Just drop the ±√ part.

In your case we are using t instead of x, but otherwise it is the same:

a = -16

b = 96

t = -96 / (2 * -16)

t = -96 / -32

t = 3

So 3 seconds after the object is thrown, it reaches its maximum height. Just calculate h(3) and you have the answer:

h(3) = -16(3²) + 96(3) + 260

I'll leave the calculation to you.

PART C:

When the object hits the ground, its height is zero, so essentially you are finding the zeros of that quadratic.

-16t² + 96t + 260 = 0

You could factor this, or just use the quadratic formula:

t = [-96 ± √(96² - 4(-16)(260)) ] / (2*-16)

You'll get two values but you can throw out the negative value.

t ≈ 8.025 seconds

P.S. The following graph may help you visualize the situation better.

You've been given height as a function of time, and all the questions are about height and time.

At time zero (t = 0) what is the height?

What is the largest value of h? (Can you differentiate h(t)?, if not, where is the vertex of the parabola?  (Let x = t - 3   ?)

When h = 0, what is t?  (solve quadratic)