Question

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

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function \( h(t) = at^2 + bt + c \), the time \( t \) at which the maximum (since \( a = -16 < 0 \)) occurs is given by \( t = -\frac{b}{2a} \).

Step2: Identify coefficients

In the function \( h(t) = -16t^2 + 96t + 6 \), we have \( a = -16 \) and \( b = 96 \).

Step3: Calculate time

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

Answer:

3 seconds (corresponding to the option: 3 seconds)