Chapter 1

A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width, as shown in the figure at the top of the next column. If the area of the pool and the path combined is 600 square meters, what is the width of the path?

A machine produces open boxes using square sheets of metal. The machine cuts equal sized squares measuring 3 inches on a side from the corners and then shapes the metal into an open box by turning up the sides. If each box must have a volume of 75 cubic inches, find the length and width of the open box.

What is a quadratic equation?

Each group member should research one situation that provides two different pricing options. These can involve areas such as public transportation options (with or without discount passes), cellphone plans, long-distance telephone plans, or anything of interest. Be sure to bring in all the details for each option. At a second group meeting, select the two pricing situations that are most interesting and relevant. Using each situation, write a word problem about selecting the better of the two options. The word problem should be one that can be solved using a linear inequality. The group should turn in the two problems and their solutions.

Explain how to solve \(x^{2}+6 x+8=0\) using factoring and the zero-product principle.

Here are two sets of ordered pairs: $$ \begin{array}{l} \operatorname{set} 1:\\{(1,5),(2,5)\\} \\ \text { set } 2:\\{(5,1),(5,2)\\} \end{array} $$ In which set is each \(x\) -coordinate paired with only one \(y\) -coordinate?

Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.

Graph \(y-2 x\) and \(y-2 x+4\) in the same rectangular coordinate system. Select integers for \(x,\) starting with \(-2\) and ending with 2

Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.

How is the quadratic formula derived?

What is the discriminant and what information does it provide about a quadratic equation?

If you are given a quadratic equation, how do you determine which method to use to solve it?

If a quadratic equation has imaginary solutions, how is this shown on the graph of \(y=a x^{2}+b x+c ?\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because I want to solve \(25 x^{2}-169=0\) fairly quickly, I'll use the quadratic formula.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I use the square root property to determine the length of a right triangle's side, I don't even bother to list the negative square root.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \((2 x-3)^{2}=25\) is equivalent to \(2 x-3=5\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Any quadratic equation that can be solved by completing the square can be solved by the quadratic formula.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The quadratic formula is developed by applying factoring and the zero-product principle to the quadratic equation \(a x^{2}+b x+c=0\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Solve for \(t: s=-16 t^{2}+v_{0} t\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A rectangular swimming pool is 12 meters long and 8 meters wide. A tile border of uniform width is to be built around the pool using 120 square meters of tile. The tile is from a discontinued stock (so no additional materials are available) and all 120 square meters are to be used. How wide should the border be? Round to the nearest tenth of a meter. If zoning laws require at least a 2 -meter-wide border around the pool, can this be done with the available tile?

Exercises \(177-179\) will help you prepare for the material covered in the next section. Factor completely: \(x^{3}+x^{2}-4 x-4\)

Exercises \(177-179\) will help you prepare for the material covered in the next section. Use the special product \((A+B)^{2}=A^{2}+2 A B+B^{2}\) to multiply: \((\sqrt{x+4}+1)^{2}\)

Exercises \(177-179\) will help you prepare for the material covered in the next section. If \(-8\) is substituted for \(x\) in the equation \(5 x^{3}+11 x^{3}+2-0\) is the resulting statement true or false?