91Ó°ÊÓ

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$f(x)=2 x-x^{2}-2$$

Find the horizontal asymptote, if there is one, of the graph of each rational function. $$f(x)=\frac{12 x}{3 x^{2}+1}$$

The force of wind blowing on a window positioned at a right angle to the direction of the wind varies jointly as the area of the window and the square of the wind's speed. It is known that a wind of 30 miles per hour blowing on a window measuring 4 feet by 5 feet exerts a force of 150 pounds. During a storm with winds of 60 miles per hour, should hurricane shutters be placed on a window that measures 3 feet by 4 feet and is capable of withstanding 300 pounds of force?

The table shows the values for the current, \(I,\) in an electric circuit and the resistance, \(R\), of the circuit. $$\begin{array}{|l|l|l|l|l|l|l|l|l|}\hline I \text { (amperes) } & 0.5 & 1.0 & 1.5 & 2.0 & 2.5 & 3.0 & 4.0 & 5.0 \\\\\hline R \text { (ohms) } & 12.0 & 6.0 & 4.0 & 3.0 & 2.4 & 2.0 & 1.5 & 1.2 \\\\\hline\end{array}$$ a. Graph the ordered pairs in the table of values, with values of \(I\) along the \(x\) -axis and values of \(R\) along the \(y\) -axis. Connect the eight points with a smooth curve. b. Does current vary directly or inversely as resistance? Use your graph and explain how you arrived at your answer. c. Write an equation of variation for \(I\) and \(R,\) using one of the ordered pairs in the table to find the constant of variation. Then use your variation equation to verify the other seven ordered pairs in the table.

An equation of a quadratic function is given. a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range. $$f(x)=2 x^{2}-8 x-3$$

What does it mean if two quantities vary directly?

What does it mean if two quantities vary inversely?

Solve each polynomial inequality and graph the solution set on a real number line. Express each solution set in interval notation. $$x^{3} \leq 4 x^{2}$$

Explain what is meant by combined variation. Give an example with your explanation.

Explain what is meant by joint variation. Give an example with your explanation.