Beginning Algebra, 11th Edition

CHAPTER 9 Review Exercises 591

9.5 More on Graphing Quadratic

Equations; Quadratic Functions

To graph

Step 1 Find the vertex: Find yby substi-
tuting this value for xin the equation.

x=- 2 ba.

yax^2 bxc, Graph

The vertex is

The y-intercept is

or

or

or

The x-intercepts are and

x

y

–2

–2

–4

–6

2

2

4

y = 2x^2 – 5x – 3 (^54 , –^498 )

A- 21 , 0B 13 , 0 2.

x=- x= 3

1

2

2 x=- 1 x= 3

2 x+ 1 = 0 x - 3 = 0

0 = 12 x+ 121 x- 32

0 = 2 x^2 - 5 x- 3

10 , - 32.

y= 21022 - 5102 - 3 =- 3

A^54 , -^498 B.

y=-

49

8

y=

25

8

• 
  

50

8

• 
  

24

8

x=

5

4

y= 2 a

25

16

b-

25

4

x=- - 3

• 5
  2122

y= 2 a

5

4

b

2

• 5 a

5

4

x=- b- 3

b

2 a

y= 2 x^2 - 5 x-3.

CONCEPTS EXAMPLES

Step 2 Find the y-intercept. Let x= 0 and solve for y.

Step 3 Find the x-intercepts (if they exist). Let
and solve for x.

y= 0

Step 4 Plot the intercepts and the vertex.

Step 5 Find and plot additional ordered pairs near the
vertex and intercepts as needed.

xy

0

0

2

30

• 5

(^54) - (^498)

• 3
  -^12

REVIEW EXERCISES

CHAPTER 9

9.1 Solve each equation by using the square root property. Give only real number solutions.

Express all radicals in simplest form.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
         
         
         4. 
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 1 r- 322 = 10 6. 12 p+ 122 = 14 7. 13 x+ 222 =- 3 8. 13 - 5 x 22 = 8

z^2 = 144 x^2 = 37 m^2 = 128 1 x+ 222 = 25