8-A10
Using Factoring to Solve Quadratic Word Problems
Algebra 8H
Show all work neatly on binder paper. Label your variables, write a quadratic equation, solve, and then
answer the problem. Remember, word problems need word answers.
1.
A positive number is 30 less than its square. Find the number.
2.
Find 2 consecutive positive odd integers whose product is 143.
3.
The sum of the squares of 2 consecutive negative even integers is 100. Find them.
4.
The length of a rectangle is 8 cm greater than its width. Find the dimensions of the rectangle if its
area is 105 cm2.
5.
The length of a rectangle is 6 cm less than twice its width. Find the dimensions of the rectangle if its
area is 108 cm2.
6.
Find the dimensions of a rectangle whose perimeter is 46 cm and whose area is 126 cm2.
(Hint: Let the width be w. Use the perimeter to find the length in terms of w).
7.
Originally the dimensions of a rectangle were 20 cm by 23 cm. When both dimensions were decreased
by the same amount, the area of the rectangle decreased by 120 cm2. Find the dimensions of the new
rectangle.
8.
Originally a rectangle was twice as long as it was wide. When 4m were added to its length and 3m
subtracted from its width, the resulting rectangle had an area of 600m2. Find the dimensions of the
new rectangle.
In exercises 9 - 14, use the formula h   4.9t2  vt  s where h is in meters and the formula
h   16t2  vt  s when h is in feet. (h = height, v = initial velocity, t = time in seconds)
9.
A ball is thrown upward with an initial speed of 24.5 m/s. When is it 19.6 m high? (2 answers)
10. A watermelon is dropped from a bridge that is 208 feet high.
watermelon to hit the water under the bridge?
How long will it take for the
11. A park has a vertical motion ride where passengers are launched straight upward from ground level
with an initial velocity of 96 ft/s. How many seconds after launch will the car reach 144 ft.?
12. Mitch tossed an apple up to Kathy, who was on a balcony 40 ft. above him, with an initial speed of 56
ft/s. Kathy missed the apple on the way up, but caught it on its way down. How long was the apple in
the air?
13. A rocket is fired upward with an initial velocity of 160 ft/s.
a. When is the rocket 400 ft. high?
b. How do you know that 400 ft. is the greatest height the rocket reaches?
14. A rocket is fired upward with an initial speed of 1960 m/s. after how many minutes does it hit the
ground.
8H 8-A10 Word Problem Handout
Key:
1. x  x 2  30 ; x = 6
2. x( x  2) 143 11, 13
3. x2  ( x  2)2 100 -8, -6
4. x( x  8) 105
7cm by 15cm
5. x(2 x  6) 108 9cm by 12cm
6. w(23 – w) = 126 9m by 14 m
7. (20  x)(23  x)  (20)(23) 120 17cm by 20 cm
8. (2w  4)(w  3)  600 40m by 15m
9. 19.6   4.9t 2  24.5t ; 4.9t 2  24.5t 19.6  0 ; 4.9(t 2 5t  4)  0
10. 0   16t 2  208 ; -16(t 2 – 13) = 0 ; t 2 – 13 = 0 ; t =
11. 144   16t 2  96t ; 16t 2  96t 144  0; 16(t 2  6t  9)  0
1 second and 4 seconds
 13  3.61sec
(time can only be positive)
3 seconds
12. 40   16t 2  56t ; 16t 2  56t  40  0 ; 8(2t 2  7t  5)  0; (2t  5)(t 1)  0 t  1 on the way up, and
5
t  (2.5 s) on the way down. The apple was in the air for 2.5 seconds.
2
13. 400   16t 2 160t ; 16t 2 160t  400  0 ; 16(t 2 10t  25)  0
The rocket hits 400 ft in 5 seconds. There is only one time that the rocket hits 400 ft. (at the
top of its peak).
14. 0   4.9t 2 1960t ; 4.9t (t  400)  0
The rocket hits the ground after 400 seconds or 6 min. and 40 sec.