Beginning Algebra, 11th Edition

13.Concept Check A student writes the quadratic formula as

.

WHAT WENT WRONG?Explain the error, and give the correct formula.

14.To solve the quadratic equation , we might choose to use ,

, and. Or, we might decide to first multiply both sides by , obtaining the

equation , and then use , , and. Show that in

either case we obtain the same solution set.

Use the quadratic formula to solve each equation. Simplify all radicals, and write all answers

in lowest terms. See Examples 2– 4.

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        38. 
            
        
        
        
        
    
    
    
    

Use the quadratic formula to solve each equation. (a)Give solutions in exact form, and

(b)use a calculator to give solutions correct to the nearest thousandth.

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Use the quadratic formula to solve each equation. See Example 5.

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Solve each problem.

53.Solve the formula for rby writing it in the form and

then using the quadratic formula. (Leave in your answer.)

54.Solve the formula for r, using the method described in Exercise 53.

(Leave in your answer.)

55.A frog is sitting on a stump 3 ft above the ground. He hops off

the stump and lands on the ground 4 ft away. During his leap,

his height hwith respect to the ground is given by

where xis the distance in feet from the base of the stump and his in feet. How far was the

frog from the base of the stump when he was 1.25 ft above the ground?

h=-0.5x^2 +1.25x+3,



V=pr^2 h+pR^2 h



S= 2 prh+pr^2 ar^2 +br+c= 0

0.6x-0.4x^2 =- 1 0.25x+0.5x^2 =1.5

0.5x^2 =x+0.5 0.25x^2 =-1.5x- 1

1

3

x^2 +

8

9

x+

7

9

= 0

3

8

x^2 - x+

17

24

= 0

2

3

z^2 -

4

9

z=

1

3

1

2

x^2 +

1

6

x= 1

2

5

x^2 -

3

5

x- 1 = 0

3

2

k^2 - k-

4

3

= 0

2 x^2 = 5 - 2 x 5 x^2 = 3 - x x^2 = 1 +x x^2 = 2 + 4 x

3 x^2 + 2 x+ 8 = 0 1 x+ 321 x+ 22 = 15 12 x+ 121 x+ 12 = 7

• 2 x^2 =- 3 x+ 2 - x^2 =- 5 x+ 20 2 x^2 +x+ 5 = 0

16 x^2 - 9 = 0 3 x^2 - 2 x+ 5 = 10 x+ 1 4 x^2 - x+ 4 =x+ 7

x^2 - 24 = 0 z^2 - 96 = 0 25 x^2 - 4 = 0

4 n^2 - 12 n= 0 7 x^2 = 12 x 9 r^2 = 11 r

2 x^2 = 5 + 3 x 2 z^2 = 30 + 7 z 6 x^2 + 6 x= 0

5 m^2 +m= 1 p^2 - 4 p+ 4 = 0 x^2 - 10 x+ 25 = 0

k^2 + 12 k- 13 = 0 r^2 - 8 r- 9 = 0 2 x^2 + 12 x=- 5

2 x^2 + 4 x- 3 = 0 a= 2 b= 4 c=- 3

b=- 4 c= 3 - 1

• 2 x^2 - 4 x+ 3 = 0 a=- 2

x=-b

2 b^2 - 4 ac

2 a

572 CHAPTER 9 Quadratic Equations

(0, 3)

(4, 0)

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