Chapter 1

Describe the relationship between the real solutions of \(a x^{2}+b x+c=0\) and the graph of \(y=a x^{2}+b x+c\)

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. I obtained \(-17\) for the discriminant, so there are two imaginary irrational solutions.

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 \(a x^{2}+b x+c=0\)

Write a quadratic equation in general form whose solution set is \(\\{-3,5\\}\).

Solve for \(t: \quad s=-16 t^{2}+v_{0} t\).

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 -meterwide border around the pool, can this be done with the available tile?

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

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: \((\sqrt{x+4}+1)^{2}\).

Will help you prepare for the material covered in the next section. If \(-8\) is substituted for \(x\) in the equation \(5 x^{\frac{2}{3}}+11 x^{\frac{1}{3}}+2=0\) is the resulting statement true or false?