Two missiles, A and B, are shot from two different launch pads. The path of missile A can be represented by the quadratic function A(t) = −2(t − 20)2 + 729, where height, A(t), is in meters, and time, t, is in seconds. The path of missile B is shown below.

Part A: What is the maximum height reached by missile A? Explain your answer.

Part B: What is the maximum height reached by missile B? Explain your answer.

Part C: Which missile reaches the highest altitude? Show your work to determine how much higher it travels.

Question

Two missiles, A and B, are shot from two different launch pads. The path of missile A can be represented by the quadratic function A(t) = −2(t − 20)2 + 729, where height, A(t), is in meters, and time, t, is in seconds. The path of missile B is shown below.

Part A: What is the maximum height reached by missile A? Explain your answer.

Part B: What is the maximum height reached by missile B? Explain your answer.

Part C: Which missile reaches the highest altitude? Show your work to determine how much higher it travels.

Mercury · Answer

part A): consider the general vertex form

f(x) = (x-h)^2 + k
where (h,k) is the vertex

compare this to A(t) = −2(t − 20)^2+ 729 to determine the vertex of A(t). the y-coordinate of the vertex is the height.

Mercury · Answer

part B): missing diagram, but assuming it's a graph of the projectile motion of missile B, simply look for the peak/vertex of the graph, then look on the y-axis to see what the corresponding height is

Mercury · Answer

part C): simply report whichever quantity from parts A vs B is higher

since it also asks "how much higher" simply subtract the higher quantity - the lower quantity