Solve . Explain or show your reasoning.

Here is one way to solve the equation  . Explain what is done in each step.

Diego and Jada are working together to solve the quadratic equation .

Jada asks Diego why he divides each side by 2 and he says, “I want to find a number that equals 100 when multiplied by itself. That number is half of 100.”

1. What mistake is Diego making?
2. If you were Jada, what could you say to Diego to help him realize his mistake?

A billboard installer accidentally drops a tool while working on a billboard. The height of the tool  seconds after it is dropped is given by the function , where is in feet.

1. Find . Explain what this value means in this situation.
2. Find . What does this value tell us about the situation?
3. Is the tool still in the air 4 seconds after it is dropped? Explain how you know.

A zoo offers unlimited drink refills to visitors who purchase its souvenir cup. The cup and the first fill cost $10, and refills after that are $2 each. The expression represents the total cost of the cup and refills.

1. A family visited the zoo several times over a summer. That summer, they paid $30 for one cup and multiple refills. How many refills did they buy?
2. A visitor has $18 to spend on drinks at the zoo today and buys a souvenir cup. How many refills can they afford during the visit?
3. Another visitor spent $10 on this deal. Did they buy any refills? Explain how you know.