Question

florencia and eli each dropped a football from different heights.
the height of florencia’s football (in feet) can be described by the following function, where ( x ) is the number of seconds since she dropped the football.
( f(x) = -16x^2 + 15 )
the height of eli’s football can be described by the following graph.
graph of a parabola with vertex at (0, 17) and x-intercepts at -1 and 1
whose football was dropped from a higher point?
\\( \circ \\) florencia
\\( \circ \\) eli

Explanation:

Step1: Find Florencia's initial height

For Florencia's function \( f(x) = -16x^2 + 15 \), the initial height (when \( x = 0 \), since \( x \) is time in seconds) is found by substituting \( x = 0 \) into the function.
\( f(0) = -16(0)^2 + 15 = 15 \) feet.

Step2: Find Eli's initial height

For Eli's football, the graph is a parabola. The initial height (when \( x = 0 \), time \( = 0 \)) is the \( y \)-intercept of the graph. From the graph, when \( x = 0 \), the \( y \)-value (height) is 17 feet (since the vertex is at \( (0, 17) \) approximately, looking at the graph's \( y \)-axis at \( x = 0 \)).

Step3: Compare the initial heights

Florencia's initial height is 15 feet, and Eli's initial height is 17 feet. Since \( 17 > 15 \), Eli's football was dropped from a higher point.

Answer:

Eli