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Question 1:

Medium

A events company offers two options for party packages. Option A has a fixed cost of \$1,000.00 plus \$35.00 per person. Option B has a fixed cost of \$1,200.00 plus \$25.00 per person. How many people need to be invited for the cost of both options to be the same?
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Question 2:

Medium

An architect is designing a building in the shape of a rectangular parallelepiped and wants to maximize the area of the base of the building, considering that the total volume of the building cannot exceed 18000 m³. The length of the base of the building is always twice the width. Based on this information, what should be the measurement of the width of the base of the building for the area to be maximized?
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Question 3:

Medium

A rocket was launched into space and its height h in relation to time t is given by the quadratic function h(t) = -16t² + 64t + 80, where the height h is measured in feet and the time t in seconds. What is the maximum height that the rocket reaches and at what moment does this happen?
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Question 4:

Hard

Considering the second degree function f(x) = ax² + bx + c, where a ≠ 0, determine the possible inputs and outputs of the function and identify the characteristics of the graph of this function.
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Question 5:

Medium

A metal bridge, in the shape of a parabolic arch, will be built. Its support will be made with six metal suspensions, three on each side, 30 meters apart from each other, as shown in the figure below. Knowing that the bridge is 40 meters high, how many meters of suspensions will be necessary for the construction of this bridge?
Source: CMRJ