4.8 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 45m 2. Find the length and width of the hall.

Equation: w (5w) = 45 5w 2 = 45 5w 2 – 45 = 0 5( w 2 – 9) = 0 5(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.

Let x, x+2, x+4 are three consecutive odd integers Equation: x (x+4) = (x+2) + 16 x 2 + 4x = x x 2 + 4x = x + 18 x 2 + 4x – x – 18 = 0 x 2 + 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

Pythagorean Formula a 2 + b 2 = c 2 Hypotenuse c Leg a Leg b

3) Peter and Mary left their house to go to work one morning. Peter has to travel north and Mary has to travel east. When Peter is 3 miles less than Mary’s distance from the office, the distance between them is 3 miles longer than Mary’s distance form the office. Find their distance from the office and the distance between them.

3) Peter and Mary left their house to go to work one morning. Peter has to travel north and Mary has to travel east. When Peter is 3 miles less than Mary’s distance from their home, the distance between them is 3 miles longer than Mary’s distance from their home. Find their distance from their home and the distance between them. Equation: x 2 + (x-3) 2 = (x+3) 2 Peter’s distance X - 3 Mary’s distance from home X Distance between them x+ 3

Equation: x 2 + (x-3) 2 = (x+3) 2 x 2 + x 2 – 6x + 9 = x 2 + 6x + 9 x 2 – 6x – 6x = 0 x x = 0 x (x – 12) = 0 x = 0 or x = 12 Peter X - 3 Mary X X + 3 Discard x=0 Therefore, Mary’s distance is 12 mi, Peter’s distance is = 9 mi, and the distance between them is 15mi.

4) If an object is thrown upward from ground level with an initial velocity of 64 ft per sec, its height h in feel t seconds later is h = -16 t t a)After how many seconds is the height 48ft b)After how many seconds does the object hit the ground?

a)48 = -16t t -3 = t 2 – 4t (divide both sides by -16) t 2 – 4t + 3 = 0 (t- 3) (t-1) = 0 t = 3 or t = 1 Therefore, the height is 48 ft after 1 second or after 3 seconds b) 0 = -16t t 0 = t 2 – 4t (divide both sides by -16) 0 = t (t – 4) t = 0 or t = 4 Therefore, the object hits the ground after 4 seconds.