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 the formula for the vertex of a parabola

For a quadratic function in the form \( h(t) = at^2 + bt + c \), the time \( t \) at which the vertex (maximum or minimum) occurs is given by \( t = -\frac{b}{2a} \).
Here, the function is \( h(t) = -16t^2 + 96t + 6 \), so \( a = -16 \) and \( b = 96 \).

Step2: Calculate the time \( t \)

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

Answer:

B. 3 seconds