The equation represents the height, in feet, of a potato seconds after it was launched from a mechanical device.

1. Write an equation that would allow us to find the time the potato hits the ground.
2. Solve the equation without graphing. Show your reasoning.

Priya found and as solutions to . Is she correct? Show how you know. 

Lin says she can tell that   and   are perfect squares because each expression has the following characteristics, which she saw in other perfect squares in standard form:

• The first term is a perfect square. The last term is also a perfect square.
• If we multiply a square root of the first term and a square root of the last term and then double the product, the result is the middle term.

1. Show that each expression has the characteristics Lin described.
2. Write each expression in factored form.

What are the solutions to the equation ?

Solve each equation by rewriting the quadratic expression in factored form and using the zero product property, or by completing the square. Then, check if your solutions are correct by using the quadratic formula.

The function is defined by .

1. What are the -intercepts of the graph of ?
2. Find the coordinates of the vertex of the graph of . Show your reasoning.

3. Sketch a graph of .