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Option 1: Just fill in the form with your homework question, and someone will respond shortly with an answer.

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Like us? Max/Min Problem – Maximizing Revenue, Selling Calculators

Q: Calculators are sold to students for 20 dollars each. Three hundred students are willing to buy them at that price. For every 5 dollar increase in price, there are 30 fewer students willing to buy the calculator. What selling price will produce the maximum revenue and what will the maximum revenue be?

A: . . . → Read More: Max/Min Problem – Maximizing Revenue, Selling Calculators

Completing the Square

Q: What is completing the square?

A: Completing the square is a technique used to convert from general form, , to standard form, . Why do we need to convert? Standard form is much easier to graph as a parabola.

Let’s look at some examples:

Write each function in the form

a)

. . . → Read More: Completing the Square

Completing the Square when a doesn’t equal 1

b) Convert to standard form by completing the square:

Step 1: In this case, a=2, so we need to do something different: factor out the 2, but only for the x terms:

Now take half of the b term (in this case, b=2) and square it.

Step 2: Important: Add that . . . → Read More: Completing the Square when a doesn’t equal 1

Completing the square when a is negative

c)Convert to standard form by completing the square:

Step 1: In this case, a=-2, so factor out the -2 term, but only for the x terms:

Now take half of the b term (in this case, b=(3/2)) and square it.

Step 2: Important: Add that number to the equation inside the . . . → Read More: Completing the square when a is negative

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?

Complex and Imaginary Numbers

Q: What is a complex number?

A: A complex number is a number that contains the imaginary number i.

8 + 2i is a complex number. It has a real part 8, and an imaginary part 2i.

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Q: What is an imaginary number?

A: is the imaginary number that somebody created when they . . . → Read More: Complex and Imaginary Numbers

Add or Subtract: a) b) c)

a)

b)

c)

Multiplying Complex Numbers

Multiply: a) b) c)

a)

b) Use F.O.I.L. (First Outside Inside Last) = = Recall that = = =

c) Again, we will use F.O.I.L.: = = = = = . . . → Read More: Multiplying Complex Numbers

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

Rectangular pool with walkway, find areas

Q: A rectangular pool has a stone walkway around it. The total lenghth of the pool and walkway is 3 times the total width. The walk way is 2 feet all around. a) Write an expression for the area of the pool b) Find the area of the pool when the total width is . . . → Read More: Rectangular pool with walkway, find areas