Algebra 1B - Chapter 10 - Part 2
Date
Assigned
Day
Mathlete:
Topic
Homework
(due the next day)
Mon
1/23
5
10.3 and 10.4 Part 3 Worksheet
(1 side)
10.3 and 10.4 Part 4 Worksheet (4 sides)
Tue
1/24
6
10.3 and 10.4 Part 4 Worksheet
(4 sides) continued...
10.3 and 10.4 Part 5: Word Problems (1 side)
Wed
1/25
7
10.5 Completing the Square
Solving Quadratics by Completing the Square
(10.5 Part A)
Thu
1/26
8
10.5 Completing the Square
Solving Quadratics by Completing the Square
(10.5 Part B)
Fri
1/27
9
10.5 Completing the Square
Solving Quadratics by Completing the Square
(10.5 Part C)
Mon
1/30
10
10.6 Solving Quadratics Using the
Quadratic Formula
Solving Quadratics by Using the Quadratic Formula
Worksheet (10.6)
Tue
1/31
11
10.6 Solving Quadratics Using the
Quadratic Formula
P.588: 1, 3, 5, 7, 17, 33
Wed
2/1
12
Review
P.582: 22-25
P.589: 30-33
Thu
2/2
Quiz on days 5-12
J
l• • •-•
• ir .: •
Name:
Algebra 1
10.3 and 10.4 Part 3 Worksheet
Hour:
Solving Quadratics by Factoring and Taking Square Roots Worksheet
1
maid' ,,nch graph iNith its function.
A. fx) = x —
B. AO = x 2 + 4
f(x) = 3 v2 — 5
E.
= —3x2 + 8
C. f(x) = — x 2 +
+5
E f(x)
1111111
. 11 ,
2. A bungee jumper leaves from a platform 256 ft above the ground. Write a quadratic function that gives the jumper's
height h in feet after t seconds. Then graph the function.
What is the original height of the jumper?
IIHIIIIIIII
What will the jumper's height be after l second?
What will the jumper's height be after 3 seconds?
............
.ipporilis
H
II
Iiiii nriplimi
How far will the jumper have fallen after 3 seconds?
How long before the jumper would hit the ground if she was not attached to a bungee cord?
What values make sense for the domain? What values make sense for the range?
How far has the jumper fallen from time / = 0 to t = 1?
Does the jumper fall the same distance from time t = 1 to t = 2 as she does
from time t = 0 to t = 1? Show work to support your answer.
Algebra 1
10.3 and 10.4 Part 4 Worksheet
Name:
Hour:
10.3 and 10.4 Word Problems Worksheet
1. Suppose a person is riding in a hot-air balloon, 144 feet above the ground. He drops an apple. The height of the apple
above the ground is given by the formula
h = —16t2 +144 , where h is height in feet and t is time in seconds.
a. Graph the function-.
b. What is the original height of the apple?
c. What will the height of the apple be after 4 seconds?
d. How far will the apple have fallen after 4 seconds?
e. How long after the apple is dropped will it hit the ground?
f. What values make sense for the domain?
g. What values make sense for the range?
h. How far has the apple fallen from time t = 0 to t = 1?
i. Does the apple fall the same distance from time t = 1 to t= 2 as it does from time t= 0 to t= 1?
Show work to support your answer.
2. Suppose you have a can of paint that will cover 400 ft2.
a. Find the radius of the largest circle you can paint. Round to the nearest tenth of a foot.
b. Suppose you have two cans of paint, which will cover a total of 800 ft2. Find the radius of the largest circle you
can paint. Round to the nearest tenth of a foot.
c. Does the radius of the circle double when the amount of paint doubles? Explain.
3. Suppose a squirrel is in a tree 24 ft above the ground. She drops an acorn.
a. Write a quadratic function for this situation. Then graph the function.
b.
What is a reasonable domain and range for the function?
4. Solve each equation by finding square roots.
=0
a. 3d2 — 1
12
b. 7h2 +0.12=1.24
5. Find the value of h for each triangle. If necessary, round to the nearest tenth.
b.
a.
/
20 1/2
/
120 em2
21i
6. The sides of a square are all increased by 3 cm. The area of the new square is 64 cm2 , Find the length of a side of the
original square.
7. You are building a rectangular wading pool. You want the area of the bottom to be 90 ft2. You want the length of the
pool to be 3 ft longer than twice its width. What will the dimensions of the pool be?
8. The product of two consecutive numbers is 14 less than 10 times the smaller number. Find each number.
9. Solve X2 = X and X2 = —X by factoring. What number is a solution to both equations?
10. Suppose you throw a baseball into the air with an initial upward velocity of 29 ft/s and an initial height of 6 ft. The
formula h = —16t2 + 29t + 6 gives the ball's height h in feet at time t in seconds.
A
a. The ball's height h is 0 when it is on the ground.
Find the number of seconds that pass before the ball
lands by solving 0 = —16t2 + 29t + 6.
b. Graph the related function for the equation in part (a).
Use your graph to estimate the maximum height of the ball.
11. Suppose the area of the sail shown in the photo is 110 ft2. Find the dimensions of the sail.
12. A square table has an area of 49 ft2. Find the dimensions of the table.
13. Solve the cubic equation: x3 —10x2 +24x = 0
14. You are building a rectangular patio with two rectangular openings for gardens. You have 124 one-foot-square
paving stones. Using the diagram below, what value of x would allow you to use all of the stones?
10.3 and 10.4 Part 5: Word Problems
Read each problem carefully and solve by factoring or taking square roots.
1. Find the x-intercept(s) and y-intercept(s) of the related function: 2x2 + 6x = 20. Then determine if the graph of the
related function would open up or down.
2. Set up a quadratic equation and solve it to find the side of a square with an area of 90 ft2. If necessary, round to the
nearest tenth.
3. A rectangular box has volume 280 in3. Its dimensions are 4 in. x (n + 2) in. x (n + 5) in. Find n.
Use the formula V =
!i;
Hour:
Name:
Solving Quadratics by Completing the Square (10.5 Part A)
•Solve by completing the square.
1. x2 —4x = 5
2. x2 +10x=-21
Solve by completing the square.
3. x2 +6x-91= 0
4. x2 —8x +12 = 0
Solve each equation by completing the square.
5. x2 —12x — 45 = 0
6. x2 — 4x = 60
7. x2 —2x = 48
8. x2 —6x —16 = 0
9. x2 —14x —72 = 0
10. x2 —16x+ 28= 0
Hour:
Name:
Solving Quadratics by Completing the Square (10.5 Part B)
Solve by completing the square.
1. x2 —6x = 0
2. x2 —3x =18
Solve by completing the square.
3. x2 +4x+4=0
4. x2—x-2=0
Solve each equation by completing the square.
5. x2 —7x = 0
6. x2 +5x = —6
7. x2 -4x=5
8. x2 + 4x —12 = 0
9. x2 +11x+10 = 0
10. x2 +2x =15
Hour:
Name:
Solving Quadratics by Completing the Square (10.5 Part C)
Solve each equation by completing the square.
1. 2x2 +8x =10
2. 2x2 +12x =32
3. 5x2 +5 =10x
4. 4x2 —12x = 40
5. 2x2 —16x = ---30
6. 3x2 + 6x —9 = 0
Solve each equation by completing the square.
7. 2x2 —16x + 7 = —7
8. 3x2 +30x = —48
9. Suppose you wish to section off a soccer field as shown in the diagram below. If the area of the field is 450
yd2, find the value of x.
10
X
10
10
X
10
10. A rectangle has a width of x. Its length is 10 feet longer than twice the width. Find the dimensions if its
area is 28 ft2.
Hour:
Name:
Solving Quadratics by Using the Quadratic Formula (10.6)
Solve each equation by using the quadratic formula. If necessary, round to the nearest hundredth.
1. x2 — 4x — 96 = 0
2. x2 —36 = 0
3. x2 +8x+5=0
4. 4x2 —12x —91= 0
5. x2 — x =132
6. 14x2 = 56
Solve each equation by using the quadratic formula. If necessary, round to the nearest hundredth.
7. 5x2 =17x+12
8. 4x2 —3x+6 =0
9. x2 —6x = —9
10. 2x2 +6x-8 =0
11. A rectangular painting has dimensions x and x + 10. The painting is in a frame 2 in. wide. The total area of
the picture and the frame is 144 in2. What are the dimensions of the painting?
12. A ball is thrown upward from the top of a building at a height of 44 ft with an initial upward velocity
of 10 ft/s. Use the formula h = —16t2 + vt + s to find out how long it will take for the ball to hit the ground.