quadratic formula and applications. the quadratic formula the following nine slides contain videos...
TRANSCRIPT
Quadratic Formula and Applications
The Quadratic Formula
2 cb
a
b
2
4a
The following nine slides contain videos with music to help you memorize the quadratic formula (a necessity of life).
Internet connection is required to view them.
Click here to bypass the video slides.
Video 1A (4:01)
Video 1B (3:53)
Video 2 (2:46)
Video 3 (0:32)
Video 4 (2:44)
Video 5 (0:25)
Rap 1 (2:13)
Rap 2 (3:19)
Rap 3 (2:52)
2 0 two unique real solub 4ac tions
2The Discrimina t b an 4 c
2 0 one real solution...doubleb 4a oc ro t2 0 cannot do yet (coming b 4ac soon)
22x 5x 2 0
25 4 2 2 9
2If is a perfect square, can facb 4ac tor.
2x 1 x 2 0
1x , x 2
2
2x 6x 9 0
26 4 1 9 0
x 3 x 3 0
x 3 double root
23x 5x 1 0
25 4 3 1 37 Yes
x6
35 7
22x 3x 4 0
a) Does the equation yield two unique real solutions?b) If yes to part (a), find the two solutions.
23 4 2 4 23 No
2x 6x 2 0
26 4 1 2 28 Yes
6x
2
28
6 2 7
2
3 7
Try these four:24x 2x 6 0 2x 5x 1 0
2 22x 2x 7 x 2x 2 3 2x 3x x 0
25 4 1 1 29 yes
5x
2
29
22 4 4 6 100
factorable
22 2x x 3 0
2 2x 3 x 1 0 3
x , x 12
2x 4x 5 0 24 4 1 5 4 no
2x x 3x 1 0
23 4 1 1 13 yes
3x 0, x
2
13
x 0 (double root), NF
2 23x 2x x 4 0
4 3 26x 3x 12x 0
4 3 4 3 27x 6x x 3x 12x
From Factoring Day 3:
Now becomes…
2 23x 2x x 4 0
4 3 26x 3x 12x 0
4 3 4 3 27x 6x x 3x 12x
21 4 2 4 33 Yes
1 33x 0 double root , x
4
CALCULATOR REQUIRED
A courtyard measuring 12 feet by 16 feet needs a pedestrian walkway all around it. This walkway would increase the total area to 285 square feet. What will be the width of the walkway?
12
16xx
x
x
16 2x 12 2x 285
1.5 or 1.5 feet
CALCULATOR REQUIRED
You are to take a square piece of cardboard, cut three-inch squares from each corner, and fold it into a box which has a volume of 71 cubic inches. What are the dimensions of the smallest square piece of cardboard which can be purchased to create such a box? Assume square pieces of cardboard are sold in whole inch dimensions only.
33
3
3
x – 6
x – 6
3 x 6 x 6 71 11” x 11”
CALCULATOR REQUIRED
Find all possible sets of three consecutive integers such that four times the sum of all three is two times the product of the larger two.
x x 1 x 2
4 x x 1 x 2 2 x 1 x 2
-1, 0, 14, 5, 6