the function h(t)=-16t^{2}+96t + 6 represents an object projected into the air from a cannon. the maximum…

the function h(t)=-16t^{2}+96t + 6 represents an object projected into the air from a cannon. the maximum height reached by the object is 150 feet. after how many seconds does the object reach its maximum height? 2 seconds 3 seconds 6 seconds 9 seconds

the function h(t)=-16t^{2}+96t + 6 represents an object projected into the air from a cannon. the maximum height reached by the object is 150 feet. after how many seconds does the object reach its maximum height? 2 seconds 3 seconds 6 seconds 9 seconds

Answer

Explanation:

Step1: Identify the function type

The function $h(t)=-16t^{2}+96t + 6$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 96$, $c = 6$.

Step2: Use the formula for the x - coordinate of the vertex

For a quadratic function $y=ax^{2}+bx + c$, the $t$ - value (in our case) of the vertex (which gives the time at which the object reaches its maximum height) is given by $t=-\frac{b}{2a}$. Substitute $a=-16$ and $b = 96$ into the formula: $t=-\frac{96}{2\times(-16)}$.

Step3: Calculate the value of t

First, calculate the denominator: $2\times(-16)=-32$. Then, $t=\frac{96}{32}=3$.

Answer:

3 seconds