Describe Han’s mistake. Then, find the correct solutions to the equation.

A picture is 10 inches wide by 15 inches long. The total area of the picture and a frame that is \(x\) inches thick can be modeled by the function \(A(x) = (2x+10)(2x+15)\).

1. Use function notation to write a statement for this description: the total area of the picture and a frame that is 2 inches thick is 266 square inches.
2. What is the total area if the picture has a frame that is 4 inches thick?

To solve the equation \(0 = 4x^2 -28x + 39\), Elena uses technology to graph the function \(f(x) = 4x^2 -28x + 39\). She finds that the graph crosses the \(x\)-axis at \((1.919,0)\) and \((5.081,0)\).

1. What is the name for the points where the graph of a function crosses the \(x\)-axis?
2. Use a calculator to compute \(f(1.919)\) and \(f(5.081)\).
3. Explain why 1.919 and 5.081 are approximate solutions to the equation \(0 = 4x^2 -28x + 39\) and are not exact solutions.

Which equation shows a next step in solving \(9(x-1)^2=36\) that will lead to the correct solutions?

Here is a description of the temperature at a certain location yesterday.

“It started out cool in the morning, but then the temperature increased until noon. It stayed the same for a while, until it suddenly dropped quickly! It got colder than it was in the morning, and after that, it was cold for the rest of the day.”
 
Sketch a graph of the temperature as a function of time.

Technology required.

The number of people, \(p\), who watch a weekly TV show is modeled by the equation \(p = 100,\!000 \boldcdot (1.1)^w\), where \(w\) is the number of weeks since the show first aired.

1. How many people watched the show the first time it aired? Explain how you know.
2. Use technology to graph the equation.
3. On which week does the show first get an audience of more than 500,000 people?