Question

the height of a basketball, in feet, after t seconds can be modeled by the expression -16(t - 1.2)^2 + 22.
complete the sentence below. write your answers as whole numbers or decimals.
the basketball reaches a maximum height of (square) feet after (square) seconds.

Explanation:

Step1: Identify the vertex form

The height function is given in vertex form \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. Here, the function is \( -16(t - 1.2)^2 + 22 \), so \( a=-16 \), \( h = 1.2 \), and \( k = 22 \).

Step2: Determine maximum height and time

Since \( a=-16<0 \), the parabola opens downward, so the vertex is the maximum point. The \( y \)-coordinate of the vertex (\( k \)) is the maximum height, and the \( x \)-coordinate (\( h \)) is the time when the maximum height occurs.

Answer:

The basketball reaches a maximum height of \( \boldsymbol{22} \) feet after \( \boldsymbol{1.2} \) seconds.