## Quadratic Equations in Engineering |
## CHAPTER 2 |

In this chapter, the applications of quadratic equations in engineering are introduced. It is assumed that students are familiar with this topic from their high school algebra course. A quadratic equation is a second-order polynomial equation in one variable that occurs in many areas of engineering. For example, the height of a ball thrown in the air can be represented by a quadratic equation. In this chapter, the solution of quadratic equations will be obtained by three methods: factoring, the quadratic formula, and completing the square.

Suppose a ball thrown upward from the ground with an initial velocity of 96 ft/s reaches a height *h*(*t*) after time *t* s as shown in Fig. 2.1. The height is expressed by the quadratic equation *h*(*t*) = 96 *t* − 16 *t*^{2} ft. Find the time *t* in seconds when *h*(*t*) = 80 ft.

**Solution:**

*h*(*t*) = 96 *t* − 16 *t*^{2} = 80

or

Equation (2.1) is a quadratic equation of the form *ax*^{2} + *bx* + *c* = 0 and will be solved using three different methods.

**Method 1: Factoring** Dividing equation (2.1) by 16 yields

Equation (2.2) can be factored as

(

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