Explain why \(3x^2\) can be said to be in both standard form and factored form.

Jada dropped her sunglasses from a bridge over a river. Which equation could represent the distance, \(y\), fallen in feet, as a function of time, \(t\), in seconds?

A football player throws a football. Function \(h\), given by \(h(t)=6+75t-16t^2\) describes the football’s height in feet, \(t\) seconds after it is thrown. 

Select all the statements that are true about this situation.

Technology required. Two rocks are launched straight up in the air.

• The height of Rock A is given by function \(f\), where \(f(t)=4+30t-16t^2\).
• The height of Rock B is given by function \(g\), where \(g(t)=5+20t-16t^2\).

In both functions, \(t\) is time measured in seconds and height is measured in feet. Use graphing technology to graph both equations.

1. What is the maximum height of each rock?
2. Which rock reaches its maximum height first?  Explain how you know.

The graph shows the number of grams of a radioactive substance in a sample at different times after the sample was first analyzed.

1. What is the average rate of change for the substance during the 10 year period?
2. Is the average rate of change a good measure for the change in the radioactive substance during these 10 years? Explain how you know.

Graph of a function, origin O. Horizontal axis 0 to 10, by 1’s, time since measured, years. Vertical from 0 to 40, by 5’s, radioactive substance, grams. Approximate points as follows: 0 comma 30, 1 comma 26, 2 comma 22, 3 comma 18, 4 comma 16, 5 comma 13, 5 comma 12, 7 comma 9, 8 comma 8, 9 comma 7, 10 comma 6.  

Each day after an outbreak of a new strain of the flu virus, a public health scientist receives a report of the number of new cases of the flu reported by area hospitals.

Would a linear or exponential model be more appropriate for this data? Explain how you know.

\(A(t)\) is a model for the temperature in Aspen, Colorado, \(t\) months after the start of the year. \(M(t)\) is a model for the temperature in Minneapolis, Minnesota, \(t\) months after the start of the year. Temperature is measured in degrees Fahrenheit.

A graph. The horizontal axis, month, scale from 0 to 12 by 2s. The vertical axis, average temperature, degrees Farenheit, scale from 20 to 90 by 10s. A key shows a dotted line represents Minneapolis and a solid line represents Aspen. A solid line passes through the points 1 comma 35, 2 comma 38, 4 comma 52, 6 comma 74, 7 comma 79, 8 comma 75, 9 comma 70, 11 comma 45, and 12 comma 35. A dashed line passes through the points 1 comma 25, 2 comma 29, 3 comma 41, 4 comma 59, 6 comma 79, 7 comma 85, 8 comma 80, 9 comma 72, 11 comma 40, and 12 comma 28.

1. What does \(A(8)\) mean in this situation? Estimate \(A(8)\).
2. Which city has a higher predicted temperature in February?
3. Are the two cities’ predicted temperatures ever the same? If so, when?