a rocket is launched in the air. its height in feet is given by ( h(t)=-16 t^{2}+104 t ) where ( t )…

a rocket is launched in the air. its height in feet is given by ( h(t)=-16 t^{2}+104 t ) where ( t ) represents the time in seconds after launch. interpret the coordinates of the vertex in context. answer attempt 1 out of 2 the ( x )-coordinate (or ( t )-coordinate) of the vertex is and represents the ( y )-coordinate (or ( h )-coordinate) of the vertex is and represents

a rocket is launched in the air. its height in feet is given by ( h(t)=-16 t^{2}+104 t ) where ( t ) represents the time in seconds after launch. interpret the coordinates of the vertex in context. answer attempt 1 out of 2 the ( x )-coordinate (or ( t )-coordinate) of the vertex is and represents the ( y )-coordinate (or ( h )-coordinate) of the vertex is and represents

Answer

Explanation:

Step1: Find the (t) - coordinate of the vertex

For a quadratic function (y = ax^{2}+bx + c), the formula for the (x) - coordinate (in this case (t) - coordinate) of the vertex is (t=-\frac{b}{2a}). Given (h(t)=-16t^{2}+104t), where (a=-16) and (b = 104). [t=-\frac{104}{2\times(-16)}=\frac{104}{32}=\frac{13}{4}=3.25] This (t) - value represents the time when the rocket reaches its maximum height.

Step2: Find the (h) - coordinate of the vertex

Substitute (t = 3.25) into the function (h(t)=-16t^{2}+104t). [h(3.25)=-16\times(3.25)^{2}+104\times3.25] [=-16\times10.5625 + 338] [=-169+338=169] This (h) - value represents the maximum height of the rocket.

Answer:

The (t) - coordinate of the vertex is (3.25) and represents the time (in seconds) when the rocket reaches its maximum height. The (h) - coordinate of the vertex is (169) and represents the maximum height (in feet) of the rocket.