5.8 Applications of Quadratic Equations
description
Transcript of 5.8 Applications of Quadratic Equations
![Page 1: 5.8 Applications of Quadratic Equations](https://reader036.fdocuments.net/reader036/viewer/2022082712/56813b43550346895da41be4/html5/thumbnails/1.jpg)
5.8 Applications of Quadratic Equations
![Page 2: 5.8 Applications of Quadratic Equations](https://reader036.fdocuments.net/reader036/viewer/2022082712/56813b43550346895da41be4/html5/thumbnails/2.jpg)
Steps (reviews)
• Read and underline important words and numbers
• Assign variables
• Create equation and solve equation
• Check
• State answer
![Page 3: 5.8 Applications of Quadratic Equations](https://reader036.fdocuments.net/reader036/viewer/2022082712/56813b43550346895da41be4/html5/thumbnails/3.jpg)
Problem with Geometric Figures
1) The length of a hall is five times the width. The area of the floor is 45m2. Find the length and width of the hall.
![Page 4: 5.8 Applications of Quadratic Equations](https://reader036.fdocuments.net/reader036/viewer/2022082712/56813b43550346895da41be4/html5/thumbnails/4.jpg)
• 1) The length of a hall is five times the width. The area of the floor is 45m2. Find the length and width of the hall.
• Equation:
w (5w) = 45
5w2 = 45
w2 = 9
w2 – 9 = 0
(w-3)(w+3) = 0
w = 3 or w = -3
w
5w
THEREFORE: The width is 3m and the length is 5(3) = 15m
Impossible to have negative width so discard this answer
![Page 5: 5.8 Applications of Quadratic Equations](https://reader036.fdocuments.net/reader036/viewer/2022082712/56813b43550346895da41be4/html5/thumbnails/5.jpg)
Problem with consecutive numbers
2) The product of the smallest and largest of three consecutive odd integers is 16 more than the middle integer. Find the numbers.
![Page 6: 5.8 Applications of Quadratic Equations](https://reader036.fdocuments.net/reader036/viewer/2022082712/56813b43550346895da41be4/html5/thumbnails/6.jpg)
2) The product of the smallest and largest of three consecutive odd integers is 16 more than the middle integer. Find the numbers.
Let x, x+2, x+4 are three consecutive odd integers
Equation: x (x+4) = (x+2) + 16
x2 + 4x = x + 2 + 16
x2 + 4x = x + 18
x2 + 4x – x – 18 = 0
x2 + 3x – 18 = 0
(x + 6) (x -3) = 0
x = -6 or x = 3
Therefore, the numbers are 3, 5, 7
-6 is an even number so discard this answer
![Page 7: 5.8 Applications of Quadratic Equations](https://reader036.fdocuments.net/reader036/viewer/2022082712/56813b43550346895da41be4/html5/thumbnails/7.jpg)
4) If an object is propelled upward from ground level with an initial velocity of 64 ft per sec, its height h in feel t seconds later is h = -16 t2 + 64t
a) After how many seconds is the height 48ft
b) After how many seconds does the object hit the ground?
![Page 8: 5.8 Applications of Quadratic Equations](https://reader036.fdocuments.net/reader036/viewer/2022082712/56813b43550346895da41be4/html5/thumbnails/8.jpg)
a) 48 = -16t2 + 64t -3 = t2 – 4t (divide both sides by -16) t2 – 4t + 3 = 0 (t- 3) (t-1) = 0 t = 3 or t = 1Therefore, the height is 48 ft after 1 second or after 3
seconds
b) 0 = -16t2 + 64t 0 = t2 – 4t (divide both sides by -16) 0 = t (t – 4) t = 0 or t = 4Therefore, the object hits the ground after 4 seconds.
![Page 9: 5.8 Applications of Quadratic Equations](https://reader036.fdocuments.net/reader036/viewer/2022082712/56813b43550346895da41be4/html5/thumbnails/9.jpg)
Pythagorean Formula
a2 + b2 = c2
Hypotenuse cLeg a
Leg b