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OPEN-ENDED Write two different quadratic functior in intercept form whose graphs have the axis of symmetry \(x=3\).

PROBLEM SOLVING An online music store sells about 4000 songs each day when it charges \(1 per song. For each \)0.05 increase in price, about 80 fewer songs per day are sold. Use the verbal model and quadratic function to determine how much the store should charge per song to maximize daily revenue.

PROBLEM SOLVING An electronics store sells 70 digital cameras per month at a price of \(320 each. For each \)20 decrease in price, about 5 more cameras per month are sold. Use the verbal model and quadratic function to determine how much the store should charge per camera to maximize monthly revenue.

DRAWING CONCLUSIONS Compare the graphs of the three quadratic functions. What do you notice? Rewrite the functions f and g in standard form to justify your answer. f(x) = (x + 3)(x + 1) g(x) = (x + 2)2 ? 1 h(x) = x2 + 4x + 3

USING STRUCTURE Write the quadratic function f(x) = x2 + x ? 12 in intercept form. Graph the function. Label the x-intercepts, y-intercept, vertex, and axis of symmetry.

PROBLEM SOLVING A woodland jumping mouse hops along a parabolic path given by y = ?0.2x2 + 1.3x, where x is the mouse’s horizontal distance traveled (in feet) and y is the corresponding height (in feet). Can the mouse jump over a fence that is 3 feet high? Justify your answer.

MODELING WITH MATHEMATICS The Gateshead Millennium Bridge spans the River Tyne. The arch of the bridge can be modeled by a parabola. The arch reaches a maximum height of 50 meters at a point roughly 63 meters across the river. Graph the curve of the arch. What are the domain and range? What do they represent in this situation?

THOUGHT PROVOKING You have 100 feet of fencing to enclose a rectangular garden. Draw three possible designs for the garden. Of these, which has the greatest area? Make a conjecture about the dimensions of the rectangular garden with the greatest possible area. Explain your reasoning.

MODELING WITH MATHEMATICS A kernel of popcorn contains water that expands when the kernel is heated, causing it to pop. The equations below represent the "popping volume" \(y\) (in cubic centimeters per gram) of popcorn with moisture content \(x\) (as a percent of the popcorn's weight). Hot-air popping: \(y=-0.761(x-5.52)(x-22.6)\) Hot-oil popping: \(y=-0.652(x-5.35)(x-21.8)\)a. For hot-air popping, what moisture content maximizes popping volume? What is the maximum volume? b. For hot-oil popping, what moisture content maximizes popping volume? What is the maximum volume? c. Use a graphing calculator to graph both functions in the same coordinate plane. What are the domain and range of each function in this situation? Explain.