Question

1. the height off the ground, in feet, of a squirrel leaping from a tree branch is given by the function h(x) = -16x² + 24x + 15, where x is the number of seconds after the squirrel leaps. how many seconds after leaping does the squirrel reach its maximum height? a 1.33 s b 0.50 s c 0.75 s d 1.00 s

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function \( H(x) = ax^2 + bx + c \), the x - coordinate of the vertex (which gives the time of maximum height for a downward - opening parabola, since \( a=-16<0 \) here) is given by \( x = -\frac{b}{2a} \).

Step2: Identify a and b from the function

In the function \( H(x)=-16x^{2}+24x + 15 \), we have \( a=-16 \) and \( b = 24 \).

Step3: Substitute a and b into the formula

Substitute \( a=-16 \) and \( b = 24 \) into the formula \( x=-\frac{b}{2a} \). We get \( x=-\frac{24}{2\times(-16)} \).
First, calculate the denominator: \( 2\times(-16)=-32 \). Then, \( x = -\frac{24}{-32}=\frac{24}{32}=\frac{3}{4}=0.75 \).

Answer:

C. 0.75 s