Chapter ISG, Problem 9.1.6P

To determine

To find intercept, max, model & domain of given function.

Answer to Problem 9.1.6P

Intercept: h = 12 and t-intercept = 1.15

Max: h = 13 at t = 0.25

Model: $h\left(0.25\right)=12$

Domain: $\left(-\infty ,\infty \right)$

Explanation of Solution

Given Information: $h\left(t\right)=-16t^2+8t+12$

Formula Used: Graphing Utility

Calculation:

(a)

For such equations, a graphing utility can often be used to investigate possible solutions. When a graphing utility is used to solve an equation, usually approximate solutions are obtained.

  $h\left(t\right)=-16t^2+8t+12$

Put the value of t in h, get:

t	-1	$\frac{1}{4}$	1
h	-12	13	4

  

(b)

Intercept: h = 12 and t-intercept = 1.15

(c)

Max: h = 13 at t = 0.25

(d)

Model: $h\left(t\right)=-16t^2+8t+12$

As t = 0.25

  $h\left(0.25\right)=-16{\left(0.25\right)}^2+8\times \left(0.25\right)+12$

Now,

  $h\left(0.25\right)=-4+4+12$

Hence,

  $h\left(0.25\right)=12$

(e)Domain: $\left(-\infty ,\infty \right)$