91Ó°ÊÓ

Solve the equation by using the quadratic formula where appropriate. $$4=9 x^{2}$$

Solve each problem algebraically. A rectangular shipping container has a capacity of 8000 cubic feet. It is \(40 \mathrm{ft}\) long and has equal width and height. Find the width and height of the container.

Use the method you think is the most appropriate to solve the given equation. Check your answers by using a different method. $$\frac{3 x}{x+1}+\frac{2}{x-1}=4$$

Suppose that a company's profit \(P,\) in thousands of dollars, on the sale of \(x\) items is given by the equation. $$P=x^{2}-6 x-40 \quad \text { where } x \geq 0$$ (a) Sketch the graph of this equation. Let \(x\) be the horizontal axis and \(P\) be the vertical axis. (b) Use the graph to determine the minimum profit the company earns. (c) How many items does the company sell if it experiences this minimum profit?

Solve the equation and round off your answers to the nearest hundredth. $$1.7 x^{2}-3.2 x=6.1$$

Sketch the graphs of \(y=-x^{2}\) and \(y=-3 x^{2}\) on the same coordinate system. How would you describe the effect the coefficient \(-3\) has on the graph of \(y=x^{2} ?\)

In Exercises \(1-64\), solve each of the given equations. If the equation is quadratic, use the factoring or square root method. If the equation has no real solutions, say so. $$\left(d+\frac{1}{4}\right)^{2}=\frac{9}{16}$$

Sketch the graphs of \(y=-x^{2}\) and \(y=-\frac{1}{3} x^{2}\) on the same coordinate system. How would you describe the effect the coefficient \(-\frac{1}{3}\) has on the graph of \(y=x^{2} ?\)

Multiply and simplify. $$(x-h)^{2}$$

In Exercises \(65-74\), solve the given equation. For quadratic equations, choose either the factoring method or the square root method, whichever you think is the easier to use. $$4(x+1)=\frac{9}{x+1}$$