Beginning Algebra, 11th Edition

Write each quotient in lowest terms. Simplify the radicals. See Section 8.5.

Evaluate the expression for the given values of a, b, and c. Simplify the radicals.

See Sections 1.3, 8.1, and 8.2.

53.a=1,b=2,c=- 4 54.a=9,b=30,c= 25

2 b^2 - 4 ac

8 + 232

4

6 - 245

6

4 + 228

2

8 - 623

6

PREVIEW EXERCISES

SECTION 9.3 Solving Quadratic Equations by the Quadratic Formula 567

EXERCISES 45 – 48

FOR INDIVIDUAL OR GROUP WORK

We have discussed “completing the square” in an algebraic sense.

This procedure can literally be applied to a geometric figure so

that it becomes a square.

For example, to complete the square for ,begin with a

square having a side of length x. Add four rectangles of width 1 to

the right side and to the bottom, as shown in the top figure. To

“complete the square,” fill in the bottom right corner with 16

squares of area 1 , as shown in the bottom figure.

Work Exercises 45 – 48 in order.

45.What is the area of the original square?

46.What is the area of the figure after the 8 rectangles are added?

47.What is the area of the figure after the 16 small squares are added?

48.At what point did we “complete the square”?

x^2 + 8 x

RELATING CONCEPTS

x^4

4

x

x 1

1

x

OBJECTIVES

Solving Quadratic Equations by the Quadratic Formula

9.3

1 Identify the values
of a, b, and cin a
quadratic equation.

2 Use the quadratic
formula to solve
quadratic equations.

3 Solve quadratic
equations with only
one solution.

4 Solve quadratic
equations with
fractions.

We can solve any quadratic equation by completing the square, but the method can be

tedious. In this section, we complete the square on the general quadratic equation

with Standard form

to obtain the quadratic formula,which gives the solution(s) of anyquadratic

equation.

ax^2 bxc0, aZ0,

NOTE In there is a restriction that ais not zero. If it were, the

equation would be linear, not quadratic.

ax^2 +bx+c=0,

OBJECTIVE 1 Identify the values of a, b, and cin a quadratic equation.

To solve a quadratic equation with the quadratic formula, we must first identify the

values of a, b, and cin the standard form.