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 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