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?\n2 seconds\n3 seconds\n6 seconds\n9 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?\n2 seconds\n3 seconds\n6 seconds\n9 seconds

Answer

Explanation:

Step1: Identify the function form

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

Step2: Use the formula for the vertex of a quadratic function

The $t$ - value of the vertex of a quadratic function $y = ax^{2}+bx + c$ 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