The height, in feet, of a thrown football is modeled by the equation \(f(t) = 6 + 30t - 16t^2\), where time, \(t\), is measured in seconds.

1. What does the constant 6 mean in this situation?
2. What does the \(30t\) mean in this situation?
3. How do you think the squared term \(\text-16t^2\) affects the value of the function \(f\)? What does this term reveal about the situation?

The height, in feet, of an arrow is modeled by the equation \(h(t)=(1+2t)(18-8t)\), where \(t\) is seconds after the arrow is shot.

1. When does the arrow hit the ground? Explain or show your reasoning.
2. From what height is the arrow shot? Explain or show your reasoning.

Two objects are launched into the air.

• The height, in feet, of Object A is given by the equation \(f(t)=4+32t-16t^2\).
• The height, in feet, of Object B is given by the equation \(g(t)=2.5+40t-16t^2\). In both functions, \(t\) is seconds after launch.

1. Which object was launched from a greater height? Explain how you know.
2. Which object was launched with a greater upward velocity? Explain how you know.

1. Find the \(x\)- and \(y\)-intercepts of the graph of the quadratic function defined by the equation \(y=(x+6)(x-6)\), without graphing. Explain or show your reasoning.
2. Technology required. Check your predictions by graphing \(y=(x+6)(x-6)\).