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: Identificar la función cuadrática

La función de altura es $h(t)=-16t^{2}+96t + 6$, que es una función cuadrática en la forma $y = ax^{2}+bx + c$, donde $a=-16$, $b = 96$ y $c = 6$.

Step2: Usar la fórmula del eje de simetría

El eje de simetría de una función cuadrática $y=ax^{2}+bx + c$ es dado por $t=-\frac{b}{2a}$. Sustituyendo $a=-16$ y $b = 96$: $t=-\frac{96}{2\times(-16)}$

Step3: Calcular el valor de $t$

$t=-\frac{96}{-32}=3$

Answer:

3 segundos