What are the solutions to the equation ?

Solve each equation.

Consider the expressions and .

Show that the two expressions define the same function.

Kiran saw that if the equation is true, then by the zero product property, either is 0 or is 0. He then reasoned that, if  is true, then either is equal to 72 or is equal to 72. 

Explain why Kiran’s conclusion is incorrect.

Andre wants to solve the equation . He uses a graphing calculator to graph and and finds that the graphs cross at the points and .

1. Substitute each -value that Andre found into the expression . Then evaluate the expression.
2. Why did neither solution make equal exactly 20?

Select all the solutions to the equation .

Han says this pattern of dots can be represented by a quadratic relationship because the dots are arranged in a square in each step.

Do you agree? Explain your reasoning.