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Max/Min Rectangle Problem, Maximize the Area

Q: You have 128 feet of fencing to fence a rectangular area. Find the largest possible area to enclose this amount.

A: The perimeter of the space will be 128=2w+2L, where w=width and L=length

Isolate for L: L=64-w

The formula for the area of the rectangle is A=w*L. Substitute L=64-w into the area formula . . . → Read More: Max/Min Rectangle Problem, Maximize the Area

What is the Quadratic Equation?

Q: What is the Quadratic Formula?

A: This is a very useful formula to remember, because it means you may never have to factor ever again!

Given a quadratic in standard form, ,

the Quadratic Formula allows you to solve for x, without factoring!.

The formula is:

Let’s try an example:

Solve . . . → Read More: What is the Quadratic Equation?

The Discriminant

Q: What is the discriminant?

A: The discriminant is part of the Quadratic Formula :

It is the part under the square root sign:

The discriminant is a useful quantity to compute, as it will tell you three things:

Case 1:

The discriminant is positive.

There are two real roots. . . . → Read More: The Discriminant

Consecutive Odd Integer Word Problem

Q: Three numbers are positive consecutive odd integers. If the larger two numbers have a product of 195, find all three integers.

A: Let x = the first integer Let x + 2 = the second integer (because 3 is 2 more than 1, and 5 is 2 more than 3, and so on…) . . . → Read More: Consecutive Odd Integer Word Problem