QUADRATICS
MAKE SENSE
Word Problems
Example 1
The area of a rectangle is 65 cm^2. The length is 2 less than three times the width. Find the length and the width.
To solve:
First, you need to find binomials that represent the dimensions of the rectangles.
->Let w represent the width
->Let (3w-2) represent the length
Now, solve.
A= wl
A= w (3w-2) ->Expand and simplify
A= 3w^2 - 2w
65 = 3w^2 - 2w ->We know that A=65
0 = 3w^2 - 2w - 65 ->Make one side = 0
0 = 3w^2 - 15w + 13w -65 ->Factor the complex trinomial
0 = (3w^2 - 15w) + (13w-65) ->Factor by grouping
0 = 3w (w-5) + 13 (w-5)
0 = (w-5)(3w+13)
w-5 3w+13
w=5 w=-4.33
The width is 5cm. It cannot be -4.33 because the rectangle cannot have negative dimensions.
If w=5. Find the length
3(5)-2 = 13
Therefore the dimensions are 5x13.
Example 2
The height of the ball thrown can be approximated by the formula h= -3t^2 + 12t + 36, where t is the time, in seconds, and h is the height, in metres.
a) When does the ball land on the ground?
b) What is the maximum height the ball reaches, and when does it reach its maximum height? *My video*
Example 3
1. a)Write and simplfy an expression for the area of the area of the shaded region.
b) If x=7, find the area of the shaded region. *My video*