Question

Jessica is eating a bag of sour skittles . Her friend ask her to share, and Jessica throws over an extra bag. Her friend does not catch the bag, and it hits the ground. The distance from the ground (height) for the bag of candies is modeled by the function h(t)= -16t²+32t+4 where h(t) is the height (distance from the ground in feet ) of the candies and t is the number of seconds the candies are in the air. Describe in a paragraph what the graph of this scenario would look like.

Answer 1

Answer:

A parabola opens downward with vertex at (1,20)

Step-by-step explanation:

The function that models the height of bag of candies is

$h(t) = - 16 {t}^{2} + 32t + 4$

The graph of this function is a parabola that opens downward.

To find the maximum height of the candy bag, we complete the squares to obtain the vertex form of the function.

Factor -16 to get;

$h(t) = - 16( {t}^{2} - 2t) + 4$

Add and subtract the square of half the coefficient of t.

$h(t) = - 16( {t}^{2} - 2t + 1) + 16+ 4$

Factor the perfect square trinomial:

$h(t) = - 16( {t - 1)}^{2} + 20$

The vertex is (1,20)

This means the maximum height after 1 second is 20 feet.