Answer:
0.25 seconds
Step-by-step explanation:
First let's expand the function h:
[tex]h = -16(t- 1/4)^2 + 49[/tex]
[tex]h = -16(t^2 - t/2 + 1/16) + 49[/tex]
[tex]h = -16t^2 + 8t - 1 + 49[/tex]
[tex]h = -16t^2 + 8t + 48[/tex]
To find when the marshmallow reaches the maximum height, we can use the formula to find the vertex of the quadratic function, and the x-coordinate of the vertex is when we have the maximum height:
[tex]x_{vertex} = -b/2a[/tex]
In our equation, b = 8 and a = -16, so:
[tex]t_{vertex} = -8 / (-32) = 0.25\ seconds[/tex]
