Katherine Johnson (1918-2020) was a mathematician of African descent who worked during the 1950s and 1960s in the calculations of trajectories for NACA (currently known as NASA) missions. She used functions to mathematically represent trajectories.

In the following picture, the trajectories of a projectile and a plane are represented.

1- Take a look at the graph and answer the following questions:

1. What type of function represents the trajectory of the plane? And the projectile's trajectory?
2. What is the maximum height that the projectile reaches? What distance does it land in?
3. At which points do the two trajectories coincide?

2.   Observe three planes in the sky, the trajectories they follow are linear functions. The plane to Barcelona follows the function f(x) = 3x + 1, while the plane to Budapest is g(x) = x + 2, and the one to Cairo is h(x) = -x + 6. Draw a graph in an axis of coordinates of the three trajectories and find the points that they coincide in.