Stuart and Francisco designed a black rocket and a white rocket during an aerospace class. Both rockets were launched after class. During the launch, Stuart and Francisco recorded data of their rockets trajectories. Stuart modeled the black rockets distance from the ground, in feet, x seconds after it was launched with the graph. Francisco modeled the white rockets distance from the ground, in feet, x seconds after it was launched with the function g(x)= -16x^2 + 50x +7 . Both wanted to know what the greatest distance was from the ground for each rocket. Stuart obtained that his rockets greatest distance from the ground was [Drop down 1] while Francisco obtained a greatest distance of [Drop down 2].

In the case of Stuart it is simple, as we have a graph, we just need to see the largest y-value on the graph. We can see that it is y = 30, then for Stuart, the largest distance from the ground is 30ft.

In the case of Francisco, we need to find the maximum of:

g(x)= -16x^2 + 50x +7

Notice that this is a quadratic of negative leading coefficient, so the maximum is at the vertex.

x = -50/(2*-16) = 25/16

Evaluating the function in 25/16 we get:

g(25/16) = -16*(25/16)^2 + 50*(25/16) +7 = 46.0625 ft

If you want to learn more about quadratic functions, you can read:

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