1. Here are equations that define quadratic functions , and . Sketch a graph, by hand or using technology, that represents each equation.

   

   

   

2. Determine how many solutions each of , and has. Explain how you know.

Mai is solving the equation . She writes that the solutions are and . Han looks at her work and disagrees. He says that only is a solution. Who do you agree with? Explain your reasoning.

The graph shows a model of the number of square meters, , of a lake that is covered by algae  weeks after it was first measured.

In a second lake, the number of square meters, , covered by algae is modeled by the equation , where is the number of weeks since it was first measured.

Graph of a function on grid, origin O. Horizontal axis, time, weeks, from 0 to 6 by 1's. Vertical axis, area, square meters, from 0 to 300 by 20's. Plotted coordinates as follows: 0 comma 240, 1 comma 120, 2 comma 60, 3 comma 30, 4 comma 15, 5 comma 7 point 5, 6 comma 3 point 75.   

For which algae population model is the area decreasing more rapidly? Explain how you know.

If the equation  is true, which is also true according to the zero product property?

1. Solve the equation .
2. Show that your solution or solutions are correct.

To solve the quadratic equation , Andre and Clare wrote the following:

1. Identify the mistake each student made.
2. Solve the equation, and show your reasoning.

Decide if each equation has 0, 1, or 2 solutions, and explain how you know.