Question

Emilio throws a marshmallow into the air from his balcony. The height of the marshmallow (in feet) is represented by the equation h=?16(t?14)^2+49, where t is the time (in seconds) after he throws the marshmallow. What is the maximum height of the marshmallow?

Answer 1

Answer:

The maximum height of the marshmallow is 49 feet.

Step-by-step explanation:

The vertex form of a parabola is

$y=a(x-h)^2+k$           .... (1)

Where, (h,k) is vertex of the parabola is a is constant.

The given function is

$h=-16(t-14)^2+49$              ..... (2)

Where, h is height of the marshmallow (in feet) and t is the time (in seconds) after he throws the marshmallow.

From equation (1) and (2), we get

$a=-16,h=14,k=49$

The value of a is -16, which is less than 0. So, the given function is a downward parabola.

The vertex of a downward parabola is the point of maxima.

The value of h is 14 and the value of k is 49. So, the vertex of the parabola is (14,49). It means the maximum height of the marshmallow is 49 feet in 14 seconds.

Therefore the maximum height of the marshmallow is 49 feet.