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

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? \n○ 2 seconds \n○ 3 seconds \n○ 6 seconds \n○ 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? \n○ 2 seconds \n○ 3 seconds \n○ 6 seconds \n○ 9 seconds

Answer

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function ( h(t) = at^2 + bt + c ), the time at which the vertex (maximum or minimum) occurs is given by ( t = -\frac{b}{2a} ). Here, ( a = -16 ), ( b = 96 ).

Step2: Calculate time for maximum height

Substitute ( a = -16 ) and ( b = 96 ) into the formula: ( t = -\frac{96}{2\times(-16)} ). Simplify the denominator: ( 2\times(-16) = -32 ). Then, ( t = -\frac{96}{-32} = 3 ).

Answer:

B. 3 seconds