Select all expressions that are equivalent to .

Here are pairs of equivalent expressions—one in standard form and the other in factored form. Find the missing numbers.

1. and
2. and
3. and
4. and

Find all the values for the variable that make each equation true.

Consider the function .

1. Evaluate , writing out every step.
2. Evaluate , writing out every step. You will run into some trouble. Describe it.
3. What is a possible domain for ?

Technology required. 

When solving the equation , Priya graphs  and then looks to find where the graph crosses the -axis.

Tyler looks at her work and says that graphing is unnecessary and Priya can set up the equations and , so the solutions are and .

1. Do you agree with Tyler? If not, where is the mistake in his reasoning?
2. How many solutions does the equation have? Find out by graphing Priya’s equation.