Day 3 - 1.5 Solving Quadratic Equations by Finding Square Roots
Using Conjugates to Rationalize the Denominator
4
5 2
3
7 2
1
23. 3x2 = 75
Practice A
24. 1
x 2  12
3
2
25. x + 12 = 13
Simplify the expression.
1.
18
2.
48
3.
20
4.
98
29. 3x2 9 = 0
5.
9  3 27
30. 1 x 2  8  17
6.
12  7
26. x2 1 = 6
27. 20  x2 = 29
28. 2x2 1 = 7
2
When an object is dropped, its height h can be
determined after t seconds by using the falling object
model h = 16t2 + s where s is the initial height. Find
the time it takes an object to hit the ground when it is
dropped from a height of s feet
25
7.
8.
16
49
9
9.
100
25
10.
27
1
11.
45
3
12.
13.
14.
15.
4
5
31. s =100
32. s = 196
33. s =480
34. s =600

35. s =750
3
36. s =1200
5
37. Multiple Choice What are all the solutions to 3x2
1
+ x+ 26 =2x,22+ x2+42?
3 3
2
A.
5 6
3, 3
B.
1 5
C.  3 2 , 3 2
5 5
D. 3
Solve the equation.
16. x2 = 16
2
38. New Car From 1970 to 1990, the average cost of a
new car C (in dollars) can be approximated by the
model C = 30.5t2 + 4192 where t is the number of
years since 1970. During which year was the
average cost of a new car $7242?
17. x2 = 144
18. x2 = 121
19. x2 4 = 0
20. x2 64 = 0
21. x2 8 = 0
22. 2x2 = 32
2
1.3, 1.4, 1.5 Classwork / Homework
Simplify.
13
28
2
2.
1 3
1.
2
3.
4.
4 5
2 3
1  5
Solve using factoring or square roots for #5-15.
5.
6.
7.
8.
9.
10.
5x  405
4 x2  20 x  25
14s 2  21s  0
x2
 6  2
25
a 2  10  7a
4( x  1)2  8
2
11. n  25  0
2
Word Problems
16. A coyote is standing on a cliff 254 feet above a roadrunner.
If the coyote drops a boulder from the cliff, how much time
does the roadrunner have to move out of its way?
17. You have a rectangular vegetable garden that measures 42
feet by 8 feet. You want to double the area of the garden
by expanding the length and width by the same amount.
What is the new length and width of the garden?
12. r  2r  80
2
13. 21b  77b  5  33
2
2
14. 3w  213  0
15.
1
2
 t  1  6  8
2
18. The pressure P (in pounds per square foot) from wind
blowing at s miles per hour is given by
. What
wind speed produces a pressure of 30 lb/ ?
19. You have made a rectangular quilt that is 5 feet by 4 feet.
You want to use the remaining 10 square feet of fabric to
add a decorative border of uniform width to the quilt. What
should the width of the quilt’s border be?
3