Evaluate a Quadratic Function Given an Output

Here you will find the input for a quadratic function when the output is given.

Check Your Understanding

1. A ball is drop from the top of a building. The height, h, of the ball above ground after t seconds can be calculated using the formula
h(t) = -16t2 + 400

How many seconds will it take for the ball to hit the ground?

Hint: The ball will hit the ground when the height above ground is 0; that is, when h(t) = 0.
My answer is 400 because h(0)=-16t+400 but i keep getteng it wrong

you do not want h(0) -- that is the initial height (time t=0)

You want t when h=0. That is,

-16t^2 + 400 = 0
t^2 = 25
t = 5

ok, then according to their hint,

0 = -16t^2 + 400
16t^2 = 400
t^2= 400/16 = 25
t = √25 = 5

so it took 5 seconds

How could it possible take 400 seconds or almost 7 minutes for a ball to fall from 400 ft ???

To find the time it takes for the ball to hit the ground, we need to solve for t when h(t) = 0.

The given quadratic function is h(t) = -16t^2 + 400. We can set this function equal to 0 and solve for t.

-16t^2 + 400 = 0

To solve this equation, we can use the quadratic formula, which states that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = -16, b = 0, and c = 400. Plugging these values into the quadratic formula, we get:

t = (-0 ± √(0^2 - 4(-16)(400))) / (2(-16))

Simplifying further:

t = ± √(0 - (-25600)) / (-32)

t = ± √(25600) / (-32)

t = ± 160 / (-32)

t = ± 5

So, the equation has two solutions: t = 5 and t = -5.

However, we are dealing with time, which cannot be negative in this context. Therefore, the ball will hit the ground after 5 seconds.

Thus, the correct answer is 5 seconds, not 400.