Question

The height of a football, in feet, t seconds after it is kicked into the air off of a tee, is modeled by the function h(t) = What is the approximate maximum height of the football?

Answer 1

Answer:

Approximately, the maximum height of the football is 19.4 feet (1st option)

Explanation:

Given:

$h(t)\text{ = -16t}^2\text{ + 35t + 0.25}$

To find:

the approximate maximum height

$\begin{gathered} h\text{ = }\frac{-b}{2a} \\ k\text{ = h\lparen}\frac{-b}{2a}) \\ h\text{ = t}_{max} \\ \\ from\text{ the equation: }a\text{ = -16, b = 35, c = 0.25} \\ t_{max}\text{ = }\frac{-35}{2(-16)} \\ t_{max}\text{ =1.09375} \end{gathered}$$\begin{gathered} To\text{ get the maximum height, we will substitute t in the equation with 1.09375} \\ NB:\text{ k in the vertex represents maximum height} \\ k\text{ = h\lparen1.09375\rparen} \\ \\ substitute\text{ the value for t:} \\ h_{max}\text{ = -16\lparen1.09375\rparen}^2\text{ + 35\lparen1.09375\rparen + 0.25} \\ h_{max\text{ }}\text{ = 19.3906} \end{gathered}$

Approximately, the maximum height of the football is 19.4 feet (1st option)