Create a diagram to show that is equivalent to .

Write a or a sign in each box so the expressions on each side of the equal sign are equivalent.

Match each quadratic expression in standard form with its equivalent expression in factored form.​​​​​​

Rewrite each expression in factored form. If you get stuck, try drawing a diagram.

Which equation has exactly one solution?

The graph represents the height of a passenger car on a ferris wheel, in feet, as a function of time, in seconds since the ride starts.

Use the graph to answer these questions:

1. What is ?
2. Does have a solution? Explain how you know.
3. Describe the domain of the function.
4. Describe the range of the function.

Graph of function, origin o, no grid. Horizontal axis, time, minutes, from 0 to 60 by 10’s. Vertical axis, height, feet, from 0 to 60, by 20’s. Line starts at 0 comma 5, curves upwards and to the right until 15 comma 55. Decreases until 30 comma 5. Increases until 45 comma 55. Decreases until 60 comma 5.

Elena solves the equation by dividing both sides by to get . She says the solution is 7.

Lin solves the equation by rewriting the equation to get . When she graphs the equation , the -intercepts are and . She says the solutions are 0 and 7.

Do you agree with either of them? Explain or show how you know.

A bacteria population, , can be represented by the equation , where is the number of days since it was measured.

1. What was the population 3 days before it was measured? Explain how you know. 
2. What is the last day when the population was more than 1,000,000? Explain how you know.