Chapter 9.6, Problem 15CYU

To determine

Find and explain Eva will ever reach a height of 20 feet or not.

Answer to Problem 15CYU

Eva will not reach a height of 20 feet.

Explanation of Solution

Given:

Eva is jumping on a trampoline. Her height h in feet can be modeled by the equation $h=-16t^2+2.4t+6$ , where I is the time in seconds. Use the discriminant to determine if Eva will reach a height of 20 feet.

Concept Used:

Find the discriminant of the equation: $h=-16t^2+2.4t+6$

  $\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}\text{discriminant}:b^2-4ac$

Calculation:

  $\begin{array}{l}\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}\text{discriminant}:b^2-4ac\\ \text{Equation:}h=-16t^2+2.4t+6\\ -16t^2+2.4t+6=20[\text{Substitute}h=20]\\ \text{Standard}\text{Form}:-16t^2+2.4t-14=0\\ a=-16;b=2.4;c=-14\\ $ \text{discriminant}:b^2-4ac={(2.4)}^2-4·-16·-14=5.76-896=-890.24$\end{array}$

The discriminant is − 890.24.

Since the discriminant is negative, the equation has no real solutions.

Thus, Eva will not reach a height of 20 feet.