Real-World Applications of Quadratic Functions

Quadratic functions are used to model real-world situations. For example they are used in area problems. We will go through another very common problem, which is finding consecutive even or odd integers.

Suppose you wanted to find two consecutive positive even integers whose product is 840. How would you go about finding these two integers?

Let n be the first even integer. Therefore, n + 2 would be the next even integer. If you used n + 1 you would end up at an odd integer so you must use n + 2.

The product of these two integers would be n(n + 2) and we want this to be equal to 840. We can write the equation:

n(n + 2) = 840
n² + 2n = 840
n² + 2n – 840 = 0

Now solve for n. You can either try to factor or use the Quadratic Formula.

(n + 30)(n – 28) = 0
n = -30 or n = 28

Since you are looking for positive even integers, you can ignore n = -30.

If the first integer is equal to 28 the next even integer must equal 30.

28(30) = 840, so our answer works.