# Quadratic Formula

Application Assignment #4

(Quadratic Equations)

Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.

Part 1

Mrs. Thomas wants to do some renovations to her backyard. She wants to get a swimming pool built in the shape of the letter L. The shape is formed from two squares with side dimensions x and as shown.

A. Write down an expression for the area of the swimming pool surface.

B. The area A is to be 30 m2. Write a quadratic equation that expresses this information.

C. Find both the solutions of your equation in part (b). Show all work.

D. Which of the solutions in part (c) is the correct value of x for the pool? State briefly why you made this choice.

Part 2

Mrs. Thomas also has a garden in her yard and wants to put a 50-meter rectangular fence around it. She only needs to fence in 3 sides because the other side is alongside the house.

The width of the garden is denoted by x, and the length by y.

A. Write an expression for y in terms of x.

B. Write an expression for the area, A, of the garden, in terms of x.

C. If the area is 200 m2, find the dimensions of the garden.

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#### Solution Preview

A. Write down an expression for the area of the swimming pool surface.

It's the area of the first square, that is x times x = x^2 plus the area of the second square, which is sqrt(x)*sqrt(x) = x

So, the total area is x^2+x

B. The area A is to be 30 m2. Write a quadratic equation that expresses this information.

We found the expression for the area in the previous question, now just make it equal to 30:

x^2+x=30

or

x^2+x-30 = 0

C. Find both the solutions of your equation in part (b). Show all work.

The Quadratic Formula is to be used here. It says that for the equation ...

#### Solution Summary

The Quadratic Formula is used here. An application using equation editors are determined.