5.3 solving quadratic equations by finding square roots
TRANSCRIPT
5.3 Solving Quadratic Equations by Finding Square Roots
EXAMPLE 1 Use properties of square roots
Simplify the expression.
5= 4a.
80 516=
= 3 14b.
6 21 126= 9 14=
c.
4
81=
4
81=
2
9
d.
7
16=
7
16=
4
16
7
1. 2. 1._____________2._____________
3. 4. 1.____________2.____________
5. 6. 1._____________2._____________
7. 8. 1._____________2._____________
9. 10. 9._____________10._____________
11. 12. 9._____________10._____________
240 32
2800 1620
216 1344
3600 75
384 1764
1
4
72
64
Show all work!Simplify each of the following. Leave each answer in radical form.
GUIDED PRACTICE for Example 1
271.
3 3
982.
2 7ANSWER
ANSWER
3.
6 5
10 15
4. 8 28
14 4ANSWER
ANSWER
GUIDED PRACTICE for Example 1
5.
3
8
9
64
6. 15
4
15
2
ANSWER
ANSWER
7. 11
25
8. 36
49
11
5
7
6 ANSWER
ANSWER
EXAMPLE 2 Rationalize denominators of fractions.
Simplify (a) 5
2and 3
7 + 2
SOLUTION
(a) 5
2
2
10=
=5
2
=5
2
2
2
(b)
SOLUTION
(b)3
7 + 2=
3
7 + 2 7 – 2
7 – 2
=21 – 3 2
49 – 7 + 7 2 2 - 2
=21 – 3 2
47
EXAMPLE 3 Solve a quadratic equation
Solve 3x2 + 5 = 41.
3x2 + 5 = 41 Write original equation.
3x2 = 36 Subtract 5 from each side.
x2 = 12 Divide each side by 3.
x = + 12 Take square roots of each side.
x = + 4 3
x = + 2 3
Product property
Simplify.
- 5 -5
3 3
EXAMPLE 3 Solve a quadratic equation
ANSWER
The solutions are and 2 3 2 3–
Check the solutions by substituting them into the original equation.
3x2 + 5 = 41
3( )2 + 5 = 412 3 ?
41 = 41
3(12) + 5 = 41?
3x2 + 5 = 41
3( )2 + 5 = 41 – 2 3 ?
41 = 41
3(12) + 5 = 41?
EXAMPLE 4 Standardized Test Practice
SOLUTION
1
5(z + 3)2 = 7 Write original equation.
(z + 3)2 = 35 Multiply each side by 5.
z + 3 = + 35 Take square roots of each side.
z = –3 + 35 Subtract 3 from each side.
The solutions are –3 + and –3 – 35 35ANSWER
The correct answer is C.
GUIDED PRACTICE for Examples 2, 3, and 4GUIDED PRACTICE
Simplify the expression.
9.
5
30
6
5
10. 9
8
2
4
3
11. 17
12
51
6ANSWER
ANSWER
ANSWER
12.
399
21
19
21
– 21 – 3 5
22
13. – 6
7 – 5
8 – 2 11
5
14. 2
4 + 11
ANSWER
ANSWER
ANSWER
– 9 + 7
74
for Examples 2, 3, and 4GUIDED PRACTICE
15. – 1
9 + 7
32 + 4 3
61
16. 4
8 – 3
ANSWER
ANSWER
for Examples 2, 3, and 4GUIDED PRACTICE
17.
Solve the equation.
5x2 = 80
+ 4
18. z2 – 7 = 29
+ 6
19. 3(x – 2)2 = 40
120
32 +
ANSWER
ANSWER
ANSWER
EXAMPLE 5 Model a dropped object with a quadratic function
Science Competition
For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 50 feet. How long does the container take to hit the ground ?
SOLUTION
h = – 16t 2 + h0 Write height function. 0 = – 16t 2 + 50 Substitute 0 for h and 50 for h0.
– 50 = – 16t 2 Subtract 50 from each side.5016 = t2 Divide each side by –16.
50
16+ = t Take square roots of each side.
+ 1.8 t Use a calculator.
ANSWERReject the negative solution, –1.8, because time must be positive. The container will fall for about 1.8 seconds before it hits the ground.
Homework:
Simplifying radicals worksheet
and
Pg. 267 #47-67o, 69, 70