[size=100][size=150]Here are graphs of functions [math]f[/math] and [math]g[/math].[/size][/size][br][img]data:image/png;base64,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[/img][br][br][size=150]Each represents the height of an object being launched into the air as a function of time.[/size][br][br]Which object was launched from a higher point?[br]

Which object reached a higher point?[br]

Which object was launched with the higher upward velocity?[br]

Which object landed last?[br]

Find the zeros of the function. Show or explain your reasoning.[br]

What do the zeros tell us in this situation? Are both zeros meaningful?[br]

From what height is the ball thrown? Explain your reasoning.[br]

About when does the ball reach its highest point, and about how high does the ball go? Show or explain your reasoning.[br]

[size=150]The height in feet of a thrown football is modeled by the equation [math]f\left(t\right)=6+30t-16t^2[/math], where time [math]t[/math] is measured in seconds.[/size][br][br]What does the constant 6 mean in this situation?

What does the [math]30t[/math] mean in this situation?[br]

How do you think the squared term [math]-16t^2[/math] affects the value of the function [math]f[/math]? What does this term reveal about the situation?[br]

[size=150]The height in feet of an arrow is modeled by the equation [math]h\left(t\right)=\left(1+2t\right)\left(18-8t\right)[/math], where [math]t[/math] is seconds after the arrow is shot.[/size][br][br]When does the arrow hit the ground? Explain or show your reasoning.[br]

From what height is the arrow shot? Explain or show your reasoning.[br]

[list][size=150][*]The height, in feet, of Object A is given by the equation [math]f\left(t\right)=4+32t-16t^2[/math].[br][/*][*]The height, in feet, of the Object B is given by the equation [math]g\left(t\right)=2.5+40t-16t^2[/math]. In both functions, [math]t[/math] is seconds after launch.[/*][/size][/list][br]Which object was launched from a greater height? Explain how you know.[br]

Which object was launched with a greater upward velocity? Explain how you know.[br]

[size=150]Predict the [math]x[/math]- and [math]y[/math]-intercepts of the graph of the quadratic function defined by the expression [math]\left(x+6\right)\left(x-6\right)[/math]. [/size][br]Explain how you made your predictions.[br]

[size=150]Bank A has an annual interest rate of 5.75%, Bank B has an annual interest rate of 7.81%, and Bank C has an annual rate of 4.45%.[/size][br][br]If we graph the amount owed for each loan as a function of years without payment, predict what the three graphs would look like. Describe or sketch your prediction.[br]

Based on your graph, how much would the student owe for each loan when they graduate from college in four years?[br]

Based on your graph, if no payments are made, how much would the student owe for each loan after 10 years?[br]

[size=150]The functions [math]f[/math] and [math]g[/math] are given by [math]f\left(x\right)=13x+6[/math] and [math]g\left(x\right)=0.1\cdot\left(1.4\right)^x[/math].[/size][br] [br][br]Which function eventually grows faster, [math]f[/math] or [math]g[/math]? Explain how you know.[br]