Examples of quadratics in the "real world"

1. Modeling with
Quadratics
The product of consecutive
integers.

2. Quadratics have many appearances!
1. A rocket is fired into the air with an initial velocity of ____. The height of the
rocket may be found with ____.
2. The length of a rectangle is two more than twice the width. If the area of the
rectangle is ____, what is the length?
3. The product of two consecutive odd integers is ___. Find the larger of the
integers.

3. Here is one of my favorite types of questions
The product of two consecutive even integers is 48. Find the
smallest integer pair.

4. First, write the function
Consecutive even means one after the other, like 2 & 4.
So let x = first integer and x + 2 = second integer...
Then, x(x + 2) = 48

5. Simplify and solve by factoring and setting
factors = 0
x(x + 2) = 48
x^2 + 2x - 48 = 0
(x + 8)(x - 6) = 0
X + 8 = 0 or x - 6 = 0
X = -8 0r x = 6
X + 2 = -6 or x + 2 = 8

6. Analyze answer and place in context
The product of two consecutive even integers is 48. Find the smallest integer pair.
Since -6 and -8 are smaller than 6 and 8, that is the solution to this problem!