# Quadratic Equations, Graphs, Rational Inequalities and Word Problems

Please see the attached file for the fully formatted problems.

Includes the following Exercises:

-Quadratic Functions and Their Graphs

-Quadratic and Rational Inequalities; Equations, Functions and Inequalities

-Quadratic Equations, Functions, and Inequalities

Maximum height. If a baseball is projected upward from ground level with an initial velocity of 64 fcct per second, then its height is a function of time, given by s(t) = ? 16t2 + 64t. Graph this function for 0 < t < 4. What is the maximum height reached by the ball'?

Maximum height. If a soccer ball is kicked straight up with an initial velocity of 32 feet per second, then its height above the earth is a function of time given by s(t) = -16t2 + 32t. Graph this function for 0 < t < 2. What is the maximum height reached by this ball'?'

Minimum cost. It costs Acme Manufacturing C dollars per hour to operate its golf ball division. An analyst has determined that C is related to the number of golf balls produced per hour, x, by the equation C = 0.009x2 ? 1.8x + 100. What number of halls per hour should Acme produce to minimize the cost per hour of manufacturing these golf balls?

Maximum profit. A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the equation P = ?25x2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit'?

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#### Solution Summary

Quadratic Equations, Graphs, Rational Inequalities and Word Problems are investigated.

Intermediate Algebra : Solving Equations and Inequalities and Maximum Area of a Rectangle Given Perimeter

Solve the equation by the method of your choice. Simplify solution, if possible.

1. (3x + 5)2 = 6

Solve the following problems.

2. You have 188 feet of fencing to enclose a rectangular region. What is the maximum area?

3. An object is propelled vertically upward from the top of a 112-foot building. The quadratic function s(t) = -16t2 + 176t + 112 models the ball's height above the ground, s(t), in feet, t seconds after it was thrown. How many seconds does it take until the object finally hits the ground? Round to the nearest tenth of a second if necessary.

Solve the equation by making an appropriate substitution.

4. x4 - 14x2 - 32 = 0

Solve the rational inequality and graph the solution set on a real number line.

5. x - 6 > 0

x +1

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