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 Read the following problems and solve them:
1. The trajectory of a projectile is a parabola with the following equation: y = - x2 + 4x, and the trajectory of a plane is a line with the equation: y = 2x . Which points do they coincide in? Draw the line and the parabola to confirm the result.
2. Katherine and her team were able to determine where a ship should take off if they knew where it was landing and the places it wanted to go over. If we take the parabola y = ax2 + bx - 3, as a projectile trajectory, we want its highest point to be in (2,1) and we want it to land in (3,0), what is the equation for the trajectory? Where should it take off?