5.8 Applications of Quadratic Equations

Steps (reviews)

• Read and underline important words and numbers

• Assign variables

• Create equation and solve equation

• Check

• State answer

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.

• 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

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.

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

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?

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.

Pythagorean Formula

a2 + b2 = c2

Hypotenuse cLeg a

Leg b